[{"author":[{"full_name":"De Nooijer, Phoebe","first_name":"Phoebe","last_name":"De Nooijer"},{"first_name":"Soeren","last_name":"Terziadis","full_name":"Terziadis, Soeren"},{"first_name":"Alexandra","last_name":"Weinberger","full_name":"Weinberger, Alexandra"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana"},{"last_name":"Mchedlidze","first_name":"Tamara","full_name":"Mchedlidze, Tamara"},{"last_name":"Löffler","first_name":"Maarten","full_name":"Löffler, Maarten"},{"full_name":"Rote, Günter","last_name":"Rote","first_name":"Günter"}],"date_created":"2024-01-28T23:01:43Z","date_updated":"2024-01-29T09:45:06Z","volume":14466,"year":"2024","acknowledgement":"This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"conference":{"name":"GD: Graph Drawing and Network Visualization","start_date":"2023-09-20","location":"Isola delle Femmine, Palermo, Italy","end_date":"2023-09-22"},"doi":"10.1007/978-3-031-49275-4_2","language":[{"iso":"eng"}],"external_id":{"arxiv":["2202.12175"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2202.12175"}],"quality_controlled":"1","month":"01","publication_identifier":{"issn":["0302-9743"],"isbn":["9783031492747"],"eissn":["1611-3349"]},"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14888","title":"Removing popular faces in curve arrangements","status":"public","intvolume":" 14466","abstract":[{"text":"A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"date_published":"2024-01-06T00:00:00Z","publication":"31st International Symposium on Graph Drawing and Network Visualization","citation":{"ama":"De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2","ieee":"P. De Nooijer et al., “Removing popular faces in curve arrangements,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.","apa":"De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49275-4_2","ista":"De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14466, 18–33.","short":"P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 18–33.","mla":"De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2.","chicago":"De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” In 31st International Symposium on Graph Drawing and Network Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2."},"page":"18-33","day":"06","article_processing_charge":"No","scopus_import":"1"},{"author":[{"first_name":"Marek","last_name":"Filakovský","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","full_name":"Filakovský, Marek"},{"first_name":"Tamio Vesa","last_name":"Nakajima","full_name":"Nakajima, Tamio Vesa"},{"first_name":"Jakub","last_name":"Opršal","id":"ec596741-c539-11ec-b829-c79322a91242","orcid":"0000-0003-1245-3456","full_name":"Opršal, Jakub"},{"first_name":"Gianluca","last_name":"Tasinato","id":"0433290C-AF8F-11E9-A4C7-F729E6697425","full_name":"Tasinato, Gianluca"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli"}],"date_created":"2024-03-24T23:00:59Z","date_updated":"2024-03-25T07:45:54Z","volume":289,"year":"2024","acknowledgement":"Marek Filakovský: This research was supported by Charles University (project PRIMUS/\r\n21/SCI/014), the Austrian Science Fund (FWF project P31312-N35), and MSCAfellow5_MUNI\r\n(CZ.02.01.01/00/22_010/0003229). Tamio-Vesa Nakajima: This research was funded by UKRI EP/X024431/1 and by a Clarendon Fund Scholarship. All data is provided in full in the results section of this paper. Jakub Opršal: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Uli Wagner: This research was supported by the Austrian Science Fund (FWF project P31312-N35).","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file_date_updated":"2024-03-25T07:44:30Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","article_number":"34","conference":{"name":"STACS: Symposium on Theoretical Aspects of Computer Science","location":"Clermont-Ferrand, France","start_date":"2024-03-12","end_date":"2024-03-14"},"doi":"10.4230/LIPIcs.STACS.2024.34","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["2312.12981"]},"quality_controlled":"1","project":[{"call_identifier":"FWF","name":"Algorithms for Embeddings and Homotopy Theory","grant_number":"P31312","_id":"26611F5C-B435-11E9-9278-68D0E5697425"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"month":"03","publication_identifier":{"isbn":["9783959773119"],"eissn":["1868-8969"]},"oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":927290,"creator":"dernst","access_level":"open_access","file_name":"2024_LIPICs_Filakovsky.pdf","checksum":"0524d4189fd1ed08989546511343edf3","success":1,"date_updated":"2024-03-25T07:44:30Z","date_created":"2024-03-25T07:44:30Z","relation":"main_file","file_id":"15175"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15168","status":"public","title":"Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs","ddc":["510"],"intvolume":" 289","abstract":[{"lang":"eng","text":"A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, … , k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the \"linearly ordered chromatic number\" of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023)."}],"type":"conference","alternative_title":["LIPIcs"],"date_published":"2024-03-01T00:00:00Z","publication":"41st International Symposium on Theoretical Aspects of Computer Science","citation":{"short":"M. Filakovský, T.V. Nakajima, J. Opršal, G. Tasinato, U. Wagner, in:, 41st International Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","mla":"Filakovský, Marek, et al. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs.” 41st International Symposium on Theoretical Aspects of Computer Science, vol. 289, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.STACS.2024.34.","chicago":"Filakovský, Marek, Tamio Vesa Nakajima, Jakub Opršal, Gianluca Tasinato, and Uli Wagner. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs.” In 41st International Symposium on Theoretical Aspects of Computer Science, Vol. 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.STACS.2024.34.","ama":"Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In: 41st International Symposium on Theoretical Aspects of Computer Science. Vol 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.STACS.2024.34","ieee":"M. Filakovský, T. V. Nakajima, J. Opršal, G. Tasinato, and U. Wagner, “Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs,” in 41st International Symposium on Theoretical Aspects of Computer Science, Clermont-Ferrand, France, 2024, vol. 289.","apa":"Filakovský, M., Nakajima, T. V., Opršal, J., Tasinato, G., & Wagner, U. (2024). Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In 41st International Symposium on Theoretical Aspects of Computer Science (Vol. 289). Clermont-Ferrand, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.STACS.2024.34","ista":"Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. 2024. Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. 41st International Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical Aspects of Computer Science, LIPIcs, vol. 289, 34."},"day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1"},{"year":"2023","acknowledgement":"Andrei Krokhin and Jakub Opršal were supported by the UK EPSRC grant EP/R034516/1. Jakub Opršal has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413. Stanislav Živný was supported by a Royal Society University Research Fellowship. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper re\u001eects only the authors’ views and not the views of the ERC or the European Commission. ","department":[{"_id":"UlWa"}],"publisher":"Society for Industrial & Applied Mathematics","publication_status":"published","author":[{"first_name":"Andrei","last_name":"Krokhin","full_name":"Krokhin, Andrei"},{"full_name":"Opršal, Jakub","id":"ec596741-c539-11ec-b829-c79322a91242","orcid":"0000-0003-1245-3456","first_name":"Jakub","last_name":"Opršal"},{"first_name":"Marcin","last_name":"Wrochna","full_name":"Wrochna, Marcin"},{"last_name":"Živný","first_name":"Stanislav","full_name":"Živný, Stanislav"}],"volume":52,"date_updated":"2023-08-01T13:11:30Z","date_created":"2023-02-16T07:03:52Z","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2003.11351"}],"external_id":{"arxiv":["2003.11351"],"isi":["000955000000001"]},"oa":1,"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"isi":1,"quality_controlled":"1","doi":"10.1137/20m1378223","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"month":"01","_id":"12563","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 52","status":"public","title":"Topology and adjunction in promise constraint satisfaction","oa_version":"Preprint","type":"journal_article","issue":"1","abstract":[{"text":"he approximate graph coloring problem, whose complexity is unresolved in most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable, where c≥k. This problem naturally generalizes to promise graph homomorphism problems and further to promise constraint satisfaction problems. The complexity of these problems has recently been studied through an algebraic approach. In this paper, we introduce two new techniques to analyze the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new unconditional NP-hardness results for a significant class of approximate graph coloring and promise graph homomorphism problems.","lang":"eng"}],"citation":{"chicago":"Krokhin, Andrei, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2023. https://doi.org/10.1137/20m1378223.","short":"A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52 (2023) 38–79.","mla":"Krokhin, Andrei, et al. “Topology and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing, vol. 52, no. 1, Society for Industrial & Applied Mathematics, 2023, pp. 38–79, doi:10.1137/20m1378223.","ieee":"A. Krokhin, J. Opršal, M. Wrochna, and S. Živný, “Topology and adjunction in promise constraint satisfaction,” SIAM Journal on Computing, vol. 52, no. 1. Society for Industrial & Applied Mathematics, pp. 38–79, 2023.","apa":"Krokhin, A., Opršal, J., Wrochna, M., & Živný, S. (2023). Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/20m1378223","ista":"Krokhin A, Opršal J, Wrochna M, Živný S. 2023. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 52(1), 38–79.","ama":"Krokhin A, Opršal J, Wrochna M, Živný S. Topology and adjunction in promise constraint satisfaction. SIAM Journal on Computing. 2023;52(1):38-79. doi:10.1137/20m1378223"},"publication":"SIAM Journal on Computing","page":"38-79","article_type":"original","date_published":"2023-01-01T00:00:00Z","scopus_import":"1","keyword":["General Mathematics","General Computer Science"],"article_processing_charge":"No","day":"01"},{"file_date_updated":"2021-07-14T07:41:50Z","author":[{"last_name":"Dymond","first_name":"Michael","full_name":"Dymond, Michael"},{"last_name":"Kaluza","first_name":"Vojtech","orcid":"0000-0002-2512-8698","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","full_name":"Kaluza, Vojtech"}],"date_updated":"2023-08-14T11:26:34Z","date_created":"2021-07-14T07:01:28Z","volume":253,"acknowledgement":"This work was done while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.","year":"2023","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"month":"03","publication_identifier":{"eissn":["1565-8511"]},"doi":"10.1007/s11856-022-2448-6","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1903.05923"],"isi":["000904950300003"]},"isi":1,"quality_controlled":"1","abstract":[{"lang":"eng","text":"In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such notions also give rise to distinct equivalence classes. Put differently, we find occurrences of particularly strong divergence of separated nets from the integer lattice. Our approach generalises that of Burago and Kleiner and McMullen which takes place largely in a continuous setting. Existence of irregular separated nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞). In the present work we obtain stronger types of non-realisable densities."}],"type":"journal_article","oa_version":"Submitted Version","file":[{"content_type":"application/pdf","file_size":900422,"creator":"vkaluza","file_name":"separated_nets.pdf","access_level":"open_access","date_created":"2021-07-14T07:41:50Z","date_updated":"2021-07-14T07:41:50Z","checksum":"6fa0a3207dd1d6467c309fd1bcc867d1","relation":"main_file","file_id":"9653"}],"_id":"9652","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Highly irregular separated nets","ddc":["515","516"],"status":"public","intvolume":" 253","day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","keyword":["Lipschitz","bilipschitz","bounded displacement","modulus of continuity","separated net","non-realisable density","Burago--Kleiner construction"],"date_published":"2023-03-01T00:00:00Z","publication":"Israel Journal of Mathematics","citation":{"chicago":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” Israel Journal of Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s11856-022-2448-6.","short":"M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554.","mla":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” Israel Journal of Mathematics, vol. 253, Springer Nature, 2023, pp. 501–54, doi:10.1007/s11856-022-2448-6.","ieee":"M. Dymond and V. Kaluza, “Highly irregular separated nets,” Israel Journal of Mathematics, vol. 253. Springer Nature, pp. 501–554, 2023.","apa":"Dymond, M., & Kaluza, V. (2023). Highly irregular separated nets. Israel Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-022-2448-6","ista":"Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal of Mathematics. 253, 501–554.","ama":"Dymond M, Kaluza V. Highly irregular separated nets. Israel Journal of Mathematics. 2023;253:501-554. doi:10.1007/s11856-022-2448-6"},"article_type":"original","page":"501-554"},{"publication":"Discrete and Computational Geometry","citation":{"mla":"Arroyo Guevara, Alan M., et al. “Inserting One Edge into a Simple Drawing Is Hard.” Discrete and Computational Geometry, vol. 69, Springer Nature, 2023, pp. 745–770, doi:10.1007/s00454-022-00394-9.","short":"A.M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, T. Wiedera, Discrete and Computational Geometry 69 (2023) 745–770.","chicago":"Arroyo Guevara, Alan M, Fabian Klute, Irene Parada, Birgit Vogtenhuber, Raimund Seidel, and Tilo Wiedera. “Inserting One Edge into a Simple Drawing Is Hard.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00394-9.","ama":"Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. 2023;69:745–770. doi:10.1007/s00454-022-00394-9","ista":"Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. 2023. Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. 69, 745–770.","apa":"Arroyo Guevara, A. M., Klute, F., Parada, I., Vogtenhuber, B., Seidel, R., & Wiedera, T. (2023). Inserting one edge into a simple drawing is hard. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00394-9","ieee":"A. M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, and T. Wiedera, “Inserting one edge into a simple drawing is hard,” Discrete and Computational Geometry, vol. 69. Springer Nature, pp. 745–770, 2023."},"article_type":"original","page":"745–770","date_published":"2023-04-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","_id":"11999","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Inserting one edge into a simple drawing is hard","ddc":["510"],"intvolume":" 69","file":[{"content_type":"application/pdf","file_size":1002218,"creator":"alisjak","file_name":"2022_DiscreteandComputionalGeometry_Arroyo.pdf","access_level":"open_access","date_updated":"2022-08-29T11:23:15Z","date_created":"2022-08-29T11:23:15Z","checksum":"def7ae3b28d9fd6aec16450e40090302","success":1,"relation":"main_file","file_id":"12006"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ, it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000840292800001"],"arxiv":["1909.07347"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"doi":"10.1007/s00454-022-00394-9","language":[{"iso":"eng"}],"month":"04","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"acknowledgement":"This work was started during the 6th Austrian–Japanese–Mexican–Spanish Workshop on Discrete Geometry in June 2019 in Austria. We thank all the participants for the good atmosphere as well as discussions on the topic. Also, we thank Jan Kynčl for sending us remarks on a preliminary version of this work and an anonymous referee for further helpful comments.Alan Arroyo was funded by the Marie Skłodowska-Curie grant agreement No 754411. Fabian Klute was partially supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 612.001.651 and by the Austrian Science Fund (FWF): J-4510. Irene Parada and Birgit Vogtenhuber were partially supported by the Austrian Science Fund (FWF): W1230 and within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. Irene Parada was also partially supported by the Independent Research Fund Denmark grant 2020-2023 (9131-00044B) Dynamic Network Analysis and by the Margarita Salas Fellowship funded by the Ministry of Universities of Spain and the European Union (NextGenerationEU). Tilo Wiedera was supported by the German Research Foundation (DFG) grant CH 897/2-2.","year":"2023","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","author":[{"first_name":"Alan M","last_name":"Arroyo Guevara","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M"},{"first_name":"Fabian","last_name":"Klute","full_name":"Klute, Fabian"},{"first_name":"Irene","last_name":"Parada","full_name":"Parada, Irene"},{"full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber","first_name":"Birgit"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"},{"last_name":"Wiedera","first_name":"Tilo","full_name":"Wiedera, Tilo"}],"date_created":"2022-08-28T22:02:01Z","date_updated":"2023-08-14T12:51:25Z","volume":69,"file_date_updated":"2022-08-29T11:23:15Z","ec_funded":1},{"scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes","publication":"Journal of Graph Algorithms and Applications","citation":{"chicago":"Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” Journal of Graph Algorithms and Applications. Brown University, 2023. https://doi.org/10.7155/jgaa.00629.","short":"A.M. Arroyo Guevara, S. Felsner, Journal of Graph Algorithms and Applications 27 (2023) 433–457.","mla":"Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” Journal of Graph Algorithms and Applications, vol. 27, no. 6, Brown University, 2023, pp. 433–57, doi:10.7155/jgaa.00629.","ieee":"A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” Journal of Graph Algorithms and Applications, vol. 27, no. 6. Brown University, pp. 433–457, 2023.","apa":"Arroyo Guevara, A. M., & Felsner, S. (2023). Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00629","ista":"Arroyo Guevara AM, Felsner S. 2023. Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. 27(6), 433–457.","ama":"Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. 2023;27(6):433-457. doi:10.7155/jgaa.00629"},"article_type":"original","page":"433-457","date_published":"2023-07-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"Bundling crossings is a strategy which can enhance the readability\r\nof graph drawings. In this paper we consider good drawings, i.e., we require that\r\nany two edges have at most one common point which can be a common vertex or a\r\ncrossing. Our main result is that there is a polynomial-time algorithm to compute an\r\n8-approximation of the bundled crossing number of a good drawing with no toothed\r\nhole. In general the number of toothed holes has to be added to the 8-approximation.\r\nIn the special case of circular drawings the approximation factor is 8, this improves\r\nupon the 10-approximation of Fink et al. [14]. Our approach also works with the same\r\napproximation factor for families of pseudosegments, i.e., curves intersecting at most\r\nonce. We also show how to compute a 9/2-approximation when the intersection graph of\r\nthe pseudosegments is bipartite and has no toothed hole."}],"issue":"6","_id":"13969","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"title":"Approximating the bundled crossing number","status":"public","intvolume":" 27","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"13979","date_updated":"2023-08-07T08:00:48Z","date_created":"2023-08-07T08:00:48Z","checksum":"9c30d2b8e324cc1c904f2aeec92013a3","success":1,"file_name":"2023_JourGraphAlgorithms_Arroyo.pdf","access_level":"open_access","file_size":865774,"content_type":"application/pdf","creator":"dernst"}],"month":"07","publication_identifier":{"issn":["1526-1719"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2109.14892"]},"oa":1,"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"doi":"10.7155/jgaa.00629","language":[{"iso":"eng"}],"file_date_updated":"2023-08-07T08:00:48Z","ec_funded":1,"acknowledgement":"This work was initiated during the Workshop on Geometric Graphs in November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during the workshop. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1. An extended abstract of this paper has been published in the proceedings of WALCOM 2022 in the Springer LNCS series, vol. 13174, pages 383–395.","year":"2023","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Brown University","author":[{"full_name":"Arroyo Guevara, Alan M","orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","first_name":"Alan M"},{"full_name":"Felsner, Stefan","last_name":"Felsner","first_name":"Stefan"}],"related_material":{"record":[{"id":"11185","relation":"earlier_version","status":"public"}]},"date_updated":"2023-09-25T10:56:10Z","date_created":"2023-08-06T22:01:11Z","volume":27},{"file":[{"content_type":"application/x-zip-compressed","file_size":28684,"creator":"skoese","file_name":"Exterior Algebra and Combinatorics.zip","access_level":"closed","date_created":"2023-07-31T10:16:32Z","date_updated":"2023-07-31T10:16:32Z","checksum":"96ee518d796d02af71395622c45de03c","relation":"source_file","file_id":"13333"},{"content_type":"application/pdf","file_size":4953418,"creator":"skoese","file_name":"thesis-pdfa.pdf","access_level":"open_access","date_created":"2023-08-03T15:28:55Z","date_updated":"2023-08-03T15:28:55Z","checksum":"f610f4713f88bc477de576aaa46b114e","success":1,"relation":"main_file","file_id":"13480"}],"oa_version":"Published Version","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"13331","ddc":["510","516"],"title":"Exterior algebra and combinatorics","status":"public","abstract":[{"lang":"eng","text":"The extension of extremal combinatorics to the setting of exterior algebra is a work\r\nin progress that gained attention recently. In this thesis, we study the combinatorial structure of exterior algebra by introducing a dictionary that translates the notions from the set systems into the framework of exterior algebra. We show both generalizations of celebrated Erdös--Ko--Rado theorem and Hilton--Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms.\r\n"}],"type":"dissertation","alternative_title":["ISTA Master's Thesis"],"date_published":"2023-07-31T00:00:00Z","citation":{"chicago":"Köse, Seyda. “Exterior Algebra and Combinatorics.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:13331.","short":"S. Köse, Exterior Algebra and Combinatorics, Institute of Science and Technology Austria, 2023.","mla":"Köse, Seyda. Exterior Algebra and Combinatorics. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:13331.","ieee":"S. Köse, “Exterior algebra and combinatorics,” Institute of Science and Technology Austria, 2023.","apa":"Köse, S. (2023). Exterior algebra and combinatorics. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:13331","ista":"Köse S. 2023. Exterior algebra and combinatorics. Institute of Science and Technology Austria.","ama":"Köse S. Exterior algebra and combinatorics. 2023. doi:10.15479/at:ista:13331"},"page":"26","day":"31","has_accepted_license":"1","article_processing_charge":"No","author":[{"id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb","first_name":"Seyda","last_name":"Köse","full_name":"Köse, Seyda"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"12680"}]},"date_updated":"2023-10-04T11:54:56Z","date_created":"2023-07-31T10:20:55Z","year":"2023","publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"UlWa"}],"file_date_updated":"2023-08-03T15:28:55Z","doi":"10.15479/at:ista:13331","supervisor":[{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner"}],"degree_awarded":"MS","language":[{"iso":"eng"}],"oa":1,"month":"07","publication_identifier":{"issn":["2791-4585"]}},{"quality_controlled":"1","external_id":{"arxiv":["2201.10892"]},"oa":1,"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2201.10892","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1016/j.disc.2023.113363","publication_identifier":{"issn":["0012-365X"]},"month":"06","department":[{"_id":"UlWa"},{"_id":"GradSch"}],"publisher":"Elsevier","publication_status":"published","year":"2023","volume":346,"date_created":"2023-02-26T23:01:00Z","date_updated":"2023-10-04T11:54:57Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"13331"}]},"author":[{"last_name":"Ivanov","first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"},{"id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb","last_name":"Köse","first_name":"Seyda","full_name":"Köse, Seyda"}],"article_number":"113363","article_type":"letter_note","citation":{"short":"G. Ivanov, S. Köse, Discrete Mathematics 346 (2023).","mla":"Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” Discrete Mathematics, vol. 346, no. 6, 113363, Elsevier, 2023, doi:10.1016/j.disc.2023.113363.","chicago":"Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems for Two-Forms.” Discrete Mathematics. Elsevier, 2023. https://doi.org/10.1016/j.disc.2023.113363.","ama":"Ivanov G, Köse S. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 2023;346(6). doi:10.1016/j.disc.2023.113363","ieee":"G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,” Discrete Mathematics, vol. 346, no. 6. Elsevier, 2023.","apa":"Ivanov, G., & Köse, S. (2023). Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.disc.2023.113363","ista":"Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 346(6), 113363."},"publication":"Discrete Mathematics","date_published":"2023-06-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","intvolume":" 346","title":"Erdős-Ko-Rado and Hilton-Milner theorems for two-forms","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12680","oa_version":"Preprint","type":"journal_article","issue":"6","abstract":[{"text":"The celebrated Erdős–Ko–Rado theorem about the maximal size of an intersecting family of r-element subsets of was extended to the setting of exterior algebra in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not been settled yet. In this short note, we show that the extension of the Erdős–Ko–Rado theorem and the characterization of the equality case therein, as well as those of the Hilton–Milner theorem to the setting of exterior algebra in the simplest non-trivial case of two-forms follow from a folklore puzzle about possible arrangements of an intersecting family of lines.","lang":"eng"}]},{"doi":"10.1112/blms.12965","date_published":"2023-12-04T00:00:00Z","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["2212.04308"]},"citation":{"ama":"Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. 2023. doi:10.1112/blms.12965","ista":"Ivanov G, Naszódi M. 2023. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society.","ieee":"G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,” Bulletin of the London Mathematical Society. London Mathematical Society, 2023.","apa":"Ivanov, G., & Naszódi, M. (2023). Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12965","mla":"Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” Bulletin of the London Mathematical Society, London Mathematical Society, 2023, doi:10.1112/blms.12965.","short":"G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society (2023).","chicago":"Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial Bound.” Bulletin of the London Mathematical Society. London Mathematical Society, 2023. https://doi.org/10.1112/blms.12965."},"main_file_link":[{"url":" https://doi.org/10.1112/blms.12965","open_access":"1"}],"publication":"Bulletin of the London Mathematical Society","article_type":"original","quality_controlled":"1","publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"article_processing_charge":"Yes (via OA deal)","month":"12","day":"04","scopus_import":"1","author":[{"first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"},{"last_name":"Naszódi","first_name":"Márton","full_name":"Naszódi, Márton"}],"oa_version":"Published Version","date_updated":"2023-12-11T10:03:54Z","date_created":"2023-12-10T23:00:58Z","_id":"14660","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"M.N. was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences aswell as the National Research, Development and Innovation Fund (NRDI) grants K119670 andK131529, and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovationand Technology from the source of the NRDI as well as the ELTE TKP 2021-NKTA-62 fundingscheme","year":"2023","publisher":"London Mathematical Society","department":[{"_id":"UlWa"}],"status":"public","publication_status":"epub_ahead","title":"Quantitative Steinitz theorem: A polynomial bound","abstract":[{"lang":"eng","text":"The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set 𝑆⊂ℝ𝑑, then there are at most 2𝑑 points of 𝑆 whose convex hull contains the origin in the interior. Bárány, Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem. Let 𝑄 be a convex polytope in ℝ𝑑 containing the standard Euclidean unit ball 𝐁𝑑. Then there exist at most 2𝑑 vertices of 𝑄 whose convex hull 𝑄′ satisfies 𝑟𝐁𝑑⊂𝑄′ with 𝑟⩾𝑑−2𝑑. They conjectured that 𝑟⩾𝑐𝑑−1∕2 holds with a universal constant 𝑐>0. We prove 𝑟⩾15𝑑2, the first polynomial lower bound on 𝑟. Furthermore, we show that 𝑟 is not greater than 2/√𝑑."}],"type":"journal_article"},{"date_published":"2023-07-27T00:00:00Z","publication":"Discrete and Computational Geometry","citation":{"short":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, Discrete and Computational Geometry (2023).","mla":"Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” Discrete and Computational Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00532-x.","chicago":"Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner. “The Crossing Tverberg Theorem.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00532-x.","ama":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem. Discrete and Computational Geometry. 2023. doi:10.1007/s00454-023-00532-x","ieee":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing Tverberg theorem,” Discrete and Computational Geometry. Springer Nature, 2023.","apa":"Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., & Wagner, U. (2023). The crossing Tverberg theorem. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00532-x","ista":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2023. The crossing Tverberg theorem. Discrete and Computational Geometry."},"article_type":"original","day":"27","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13974","title":"The crossing Tverberg theorem","status":"public","abstract":[{"lang":"eng","text":"The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r−1)+1 points in Rd, one can find a partition X=X1∪⋯∪Xr of X, such that the convex hulls of the Xi, i=1,…,r, all share a common point. In this paper, we prove a trengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span ⌊n/3⌋ vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Álvarez-Rebollar et al. guarantees ⌊n/6⌋pairwise crossing triangles. Our result generalizes to a result about simplices in Rd, d≥2."}],"type":"journal_article","doi":"10.1007/s00454-023-00532-x","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1812.04911"}],"external_id":{"isi":["001038546500001"],"arxiv":["1812.04911"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF","grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425"}],"month":"07","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"author":[{"full_name":"Fulek, Radoslav","first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774"},{"first_name":"Bernd","last_name":"Gärtner","full_name":"Gärtner, Bernd"},{"full_name":"Kupavskii, Andrey","last_name":"Kupavskii","first_name":"Andrey"},{"full_name":"Valtr, Pavel","last_name":"Valtr","first_name":"Pavel"},{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"6647","relation":"earlier_version","status":"public"}]},"date_updated":"2023-12-13T12:03:35Z","date_created":"2023-08-06T22:01:12Z","year":"2023","acknowledgement":"Part of the research leading to this paper was done during the 16th Gremo Workshop on Open Problems (GWOP), Waltensburg, Switzerland, June 12–16, 2018. We thank Patrick Schnider for suggesting the problem, and Stefan Felsner, Malte Milatz, and Emo Welzl for fruitful discussions during the workshop. We also thank Stefan Felsner and Manfred Scheucher for finding, communicating the example from Sect. 3.3, and the kind permission to include their visualization of the point set. We thank Dömötör Pálvölgyi, the SoCG reviewers, and DCG reviewers for various helpful comments.\r\nR. Fulek gratefully acknowledges support from Austrian Science Fund (FWF), Project M2281-N35. A. Kupavskii was supported by the Advanced Postdoc.Mobility Grant no. P300P2_177839 of the Swiss National Science Foundation. Research by P. Valtr was supported by the Grant no. 18-19158 S of the Czech Science Foundation (GAČR).","publication_status":"epub_ahead","publisher":"Springer Nature","department":[{"_id":"UlWa"}]},{"oa_version":"Published Version","file":[{"creator":"dernst","file_size":623787,"content_type":"application/pdf","file_name":"2023_IsraelJourMath_Wagner.pdf","access_level":"open_access","date_updated":"2023-10-31T11:20:31Z","date_created":"2023-10-31T11:20:31Z","success":1,"checksum":"fbb05619fe4b650f341cc730425dd9c3","file_id":"14475","relation":"main_file"}],"_id":"14445","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 256","status":"public","ddc":["510"],"title":"Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes","issue":"2","abstract":[{"lang":"eng","text":"We prove the following quantitative Borsuk–Ulam-type result (an equivariant analogue of Gromov’s Topological Overlap Theorem): Let X be a free ℤ/2-complex of dimension d with coboundary expansion at least ηk in dimension 0 ≤ k < d. Then for every equivariant map F: X →ℤ/2 ℝd, the fraction of d-simplices σ of X with 0 ∈ F (σ) is at least 2−d Π d−1k=0ηk.\r\n\r\nAs an application, we show that for every sufficiently thick d-dimensional spherical building Y and every map f: Y → ℝ2d, we have f(σ) ∩ f(τ) ≠ ∅ for a constant fraction μd > 0 of pairs {σ, τ} of d-simplices of Y. In particular, such complexes are non-embeddable into ℝ2d, which proves a conjecture of Tancer and Vorwerk for sufficiently thick spherical buildings.\r\n\r\nWe complement these results by upper bounds on the coboundary expansion of two families of simplicial complexes; this indicates some limitations to the bounds one can obtain by straighforward applications of the quantitative Borsuk–Ulam theorem. Specifically, we prove\r\n\r\n• an upper bound of (d + 1)/2d on the normalized (d − 1)-th coboundary expansion constant of complete (d + 1)-partite d-dimensional complexes (under a mild divisibility assumption on the sizes of the parts); and\r\n\r\n• an upper bound of (d + 1)/2d + ε on the normalized (d − 1)-th coboundary expansion of the d-dimensional spherical building associated with GLd+2(Fq) for any ε > 0 and sufficiently large q. This disproves, in a rather strong sense, a conjecture of Lubotzky, Meshulam and Mozes."}],"type":"journal_article","date_published":"2023-09-01T00:00:00Z","citation":{"ieee":"U. Wagner and P. Wild, “Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes,” Israel Journal of Mathematics, vol. 256, no. 2. Springer Nature, pp. 675–717, 2023.","apa":"Wagner, U., & Wild, P. (2023). Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-023-2521-9","ista":"Wagner U, Wild P. 2023. Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. 256(2), 675–717.","ama":"Wagner U, Wild P. Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. 2023;256(2):675-717. doi:10.1007/s11856-023-2521-9","chicago":"Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap, and Crossing Numbers of Simplicial Complexes.” Israel Journal of Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s11856-023-2521-9.","short":"U. Wagner, P. Wild, Israel Journal of Mathematics 256 (2023) 675–717.","mla":"Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap, and Crossing Numbers of Simplicial Complexes.” Israel Journal of Mathematics, vol. 256, no. 2, Springer Nature, 2023, pp. 675–717, doi:10.1007/s11856-023-2521-9."},"publication":"Israel Journal of Mathematics","page":"675-717","article_type":"original","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1","author":[{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"},{"full_name":"Wild, Pascal","last_name":"Wild","first_name":"Pascal","id":"4C20D868-F248-11E8-B48F-1D18A9856A87"}],"volume":256,"date_updated":"2023-12-13T13:09:07Z","date_created":"2023-10-22T22:01:14Z","year":"2023","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","publication_status":"published","file_date_updated":"2023-10-31T11:20:31Z","doi":"10.1007/s11856-023-2521-9","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["001081646400010"]},"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["0021-2172"],"eissn":["1565-8511"]},"month":"09"},{"article_type":"original","publication":"Discrete Mathematics and Theoretical Computer Science","citation":{"chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science. EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383.","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023).","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9.","ieee":"A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383"},"date_published":"2023-01-18T00:00:00Z","scopus_import":"1","day":"18","has_accepted_license":"1","article_processing_charge":"No","ddc":["000"],"status":"public","title":"Token swapping on trees","intvolume":" 24","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"12833","file":[{"file_size":2072197,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2022_DMTCS_Biniaz.pdf","checksum":"439102ea4f6e2aeefd7107dfb9ccf532","success":1,"date_updated":"2023-04-17T08:10:28Z","date_created":"2023-04-17T08:10:28Z","relation":"main_file","file_id":"12844"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"issue":"2","quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1903.06981"]},"language":[{"iso":"eng"}],"doi":"10.46298/DMTCS.8383","month":"01","publication_identifier":{"issn":["1462-7264"],"eissn":["1365-8050"]},"publication_status":"published","publisher":"EPI Sciences","department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"UlWa"}],"year":"2023","acknowledgement":"This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n","date_updated":"2024-01-04T12:42:09Z","date_created":"2023-04-16T22:01:08Z","volume":24,"author":[{"full_name":"Biniaz, Ahmad","last_name":"Biniaz","first_name":"Ahmad"},{"full_name":"Jain, Kshitij","last_name":"Jain","first_name":"Kshitij"},{"full_name":"Lubiw, Anna","first_name":"Anna","last_name":"Lubiw"},{"first_name":"Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana"},{"last_name":"Miltzow","first_name":"Tillmann","full_name":"Miltzow, Tillmann"},{"first_name":"Debajyoti","last_name":"Mondal","full_name":"Mondal, Debajyoti"},{"last_name":"Naredla","first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty"},{"last_name":"Tkadlec","first_name":"Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef"},{"full_name":"Turcotte, Alexi","first_name":"Alexi","last_name":"Turcotte"}],"related_material":{"record":[{"id":"7950","relation":"earlier_version","status":"public"}]},"article_number":"9","file_date_updated":"2023-04-17T08:10:28Z"},{"date_created":"2024-01-08T09:48:56Z","date_updated":"2024-01-08T09:57:25Z","volume":2023,"author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov","first_name":"Grigory"},{"full_name":"Naszódi, Márton","last_name":"Naszódi","first_name":"Márton"}],"publication_status":"published","publisher":"Oxford University Press","department":[{"_id":"UlWa"}],"acknowledgement":"We thank Alexander Litvak for the many discussions on Theorem 1.1. Igor Tsiutsiurupa participated in the early stage of this project. To our deep regret, Igor chose another road for his life and stopped working with us.\r\nThis work was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences [to M.N.]; the National Research, Development, and Innovation Fund (NRDI) [K119670 and K131529 to M.N.]; and the ÚNKP-22-5 New National Excellence Program of the Ministry for Innovation and Technology from the source of the NRDI [to M.N.].","year":"2023","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","file_date_updated":"2024-01-08T09:53:09Z","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnad210","quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"external_id":{"arxiv":["2212.11781"]},"month":"12","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"file":[{"file_id":"14738","relation":"main_file","success":1,"checksum":"353666cea80633beb0f1ffd342dff6d4","date_created":"2024-01-08T09:53:09Z","date_updated":"2024-01-08T09:53:09Z","access_level":"open_access","file_name":"2023_IMRN_Ivanov.pdf","creator":"dernst","file_size":815777,"content_type":"application/pdf"}],"oa_version":"Published Version","ddc":["510"],"title":"Functional John and Löwner conditions for pairs of log-concave functions","status":"public","intvolume":" 2023","_id":"14737","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ in $\\mathbb{R}^{d}$ has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids by positions (affine images) of another body $L$. Another, more recent direction is to consider logarithmically concave functions on $\\mathbb{R}^{d}$ instead of convex bodies: we designate some special, radially symmetric log-concave function $g$ as the analogue of the Euclidean ball, and want to find its largest integral position under the constraint that it is pointwise below some given log-concave function $f$. We follow both directions simultaneously: we consider the functional question, and allow essentially any meaningful function to play the role of $g$ above. Our general theorems jointly extend known results in both directions. The dual problem in the setting of convex bodies asks for the smallest volume ellipsoid, called Löwner’s ellipsoid, containing $K$. We consider the analogous problem for functions: we characterize the solutions of the optimization problem of finding a smallest integral position of some log-concave function $g$ under the constraint that it is pointwise above $f$. It turns out that in the functional setting, the relationship between the John and the Löwner problems is more intricate than it is in the setting of convex bodies.","lang":"eng"}],"issue":"23","type":"journal_article","date_published":"2023-12-01T00:00:00Z","article_type":"original","page":"20613-20669","publication":"International Mathematics Research Notices","citation":{"ista":"Ivanov G, Naszódi M. 2023. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023(23), 20613–20669.","apa":"Ivanov, G., & Naszódi, M. (2023). Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnad210","ieee":"G. Ivanov and M. Naszódi, “Functional John and Löwner conditions for pairs of log-concave functions,” International Mathematics Research Notices, vol. 2023, no. 23. Oxford University Press, pp. 20613–20669, 2023.","ama":"Ivanov G, Naszódi M. Functional John and Löwner conditions for pairs of log-concave functions. International Mathematics Research Notices. 2023;2023(23):20613-20669. doi:10.1093/imrn/rnad210","chicago":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices. Oxford University Press, 2023. https://doi.org/10.1093/imrn/rnad210.","mla":"Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions for Pairs of Log-Concave Functions.” International Mathematics Research Notices, vol. 2023, no. 23, Oxford University Press, 2023, pp. 20613–69, doi:10.1093/imrn/rnad210.","short":"G. Ivanov, M. Naszódi, International Mathematics Research Notices 2023 (2023) 20613–20669."},"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","keyword":["General Mathematics"]},{"doi":"10.1007/s10711-023-00862-3","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.1007/s10711-023-00862-3","open_access":"1"}],"external_id":{"isi":["001105681500001"],"arxiv":["2102.13046"]},"oa":1,"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["0046-5755"],"eissn":["1572-9168"]},"month":"11","author":[{"first_name":"Michael","last_name":"Dymond","full_name":"Dymond, Michael"},{"orcid":"0000-0002-2512-8698","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","last_name":"Kaluza","first_name":"Vojtech","full_name":"Kaluza, Vojtech"}],"date_updated":"2024-01-11T13:06:32Z","date_created":"2021-07-14T07:01:27Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was started while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35. It was continued when the first named author was employed at University of Leipzig and the second named author was employed at Institute of Science and Technology of Austria, where he was supported by an IST Fellowship.","year":"2023","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"publication_status":"epub_ahead","article_number":"15","date_published":"2023-11-17T00:00:00Z","citation":{"ama":"Dymond M, Kaluza V. Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata. 2023. doi:10.1007/s10711-023-00862-3","ieee":"M. Dymond and V. Kaluza, “Divergence of separated nets with respect to displacement equivalence,” Geometriae Dedicata. Springer Nature, 2023.","apa":"Dymond, M., & Kaluza, V. (2023). Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata. Springer Nature. https://doi.org/10.1007/s10711-023-00862-3","ista":"Dymond M, Kaluza V. 2023. Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata., 15.","short":"M. Dymond, V. Kaluza, Geometriae Dedicata (2023).","mla":"Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect to Displacement Equivalence.” Geometriae Dedicata, 15, Springer Nature, 2023, doi:10.1007/s10711-023-00862-3.","chicago":"Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect to Displacement Equivalence.” Geometriae Dedicata. Springer Nature, 2023. https://doi.org/10.1007/s10711-023-00862-3."},"publication":"Geometriae Dedicata","article_type":"original","article_processing_charge":"Yes (via OA deal)","day":"17","scopus_import":"1","oa_version":"Published Version","_id":"9651","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","title":"Divergence of separated nets with respect to displacement equivalence","status":"public","abstract":[{"lang":"eng","text":"We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞). Two separated nets are called ϕ-displacement equivalent if, roughly speaking, there is a bijection between them which, for large radii R, displaces points of norm at most R by something of order at most ϕ(R). We show that the spectrum of ϕ-displacement equivalence spans from the established notion of bounded displacement equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation, coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞. We further undertake a comparison of our notion of ϕ-displacement equivalence with previously studied relations on separated nets. Particular attention is given to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz equivalence."}],"type":"journal_article"},{"author":[{"first_name":"Florestan R","last_name":"Brunck","id":"6ab6e556-f394-11eb-9cf6-9dfb78f00d8d","full_name":"Brunck, Florestan R"}],"volume":70,"date_updated":"2024-01-29T11:16:16Z","date_created":"2023-07-23T22:01:14Z","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","year":"2023","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"publication_status":"published","file_date_updated":"2024-01-29T11:15:22Z","doi":"10.1007/s00454-023-00500-5","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2107.04112"],"isi":["001023742800003"]},"isi":1,"quality_controlled":"1","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"07","file":[{"content_type":"application/pdf","file_size":1466020,"creator":"dernst","file_name":"2023_DiscreteComputGeometry_Brunck.pdf","access_level":"open_access","date_updated":"2024-01-29T11:15:22Z","date_created":"2024-01-29T11:15:22Z","checksum":"865e68daafdd4edcfc280172ec50f5ea","success":1,"relation":"main_file","file_id":"14897"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13270","intvolume":" 70","title":"Iterated medial triangle subdivision in surfaces of constant curvature","ddc":["510"],"status":"public","issue":"3","abstract":[{"lang":"eng","text":"Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into four triangles by joining the midpoints of its edges. We show the existence of a uniform δ>0\r\n such that, at any step of the subdivision, all the triangle angles lie in the interval (δ,π−δ)\r\n. Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses."}],"type":"journal_article","date_published":"2023-07-05T00:00:00Z","citation":{"apa":"Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00500-5","ieee":"F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant curvature,” Discrete and Computational Geometry, vol. 70, no. 3. Springer Nature, pp. 1059–1089, 2023.","ista":"Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 70(3), 1059–1089.","ama":"Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature. Discrete and Computational Geometry. 2023;70(3):1059-1089. doi:10.1007/s00454-023-00500-5","chicago":"Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00500-5.","short":"F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089.","mla":"Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature.” Discrete and Computational Geometry, vol. 70, no. 3, Springer Nature, 2023, pp. 1059–89, doi:10.1007/s00454-023-00500-5."},"publication":"Discrete and Computational Geometry","page":"1059-1089","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"05","scopus_import":"1"},{"language":[{"iso":"eng"}],"doi":"10.1145/3559736.3559740","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/2208.13538","open_access":"1"}],"external_id":{"arxiv":["2208.13538"]},"oa":1,"publication_identifier":{"issn":["2372-3491"]},"month":"07","volume":9,"date_created":"2022-08-27T11:23:37Z","date_updated":"2022-09-05T08:19:38Z","author":[{"last_name":"Krokhin","first_name":"Andrei","full_name":"Krokhin, Andrei"},{"full_name":"Opršal, Jakub","first_name":"Jakub","last_name":"Opršal","id":"ec596741-c539-11ec-b829-c79322a91242","orcid":"0000-0003-1245-3456"}],"department":[{"_id":"UlWa"}],"publisher":"Association for Computing Machinery","publication_status":"published","year":"2022","date_published":"2022-07-01T00:00:00Z","page":"30-59","article_type":"original","citation":{"chicago":"Krokhin, Andrei, and Jakub Opršal. “An Invitation to the Promise Constraint Satisfaction Problem.” ACM SIGLOG News. Association for Computing Machinery, 2022. https://doi.org/10.1145/3559736.3559740.","mla":"Krokhin, Andrei, and Jakub Opršal. “An Invitation to the Promise Constraint Satisfaction Problem.” ACM SIGLOG News, vol. 9, no. 3, Association for Computing Machinery, 2022, pp. 30–59, doi:10.1145/3559736.3559740.","short":"A. Krokhin, J. Opršal, ACM SIGLOG News 9 (2022) 30–59.","ista":"Krokhin A, Opršal J. 2022. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 9(3), 30–59.","apa":"Krokhin, A., & Opršal, J. (2022). An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. Association for Computing Machinery. https://doi.org/10.1145/3559736.3559740","ieee":"A. Krokhin and J. Opršal, “An invitation to the promise constraint satisfaction problem,” ACM SIGLOG News, vol. 9, no. 3. Association for Computing Machinery, pp. 30–59, 2022.","ama":"Krokhin A, Opršal J. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 2022;9(3):30-59. doi:10.1145/3559736.3559740"},"publication":"ACM SIGLOG News","article_processing_charge":"No","day":"01","oa_version":"Preprint","intvolume":" 9","status":"public","title":"An invitation to the promise constraint satisfaction problem","_id":"11991","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","abstract":[{"lang":"eng","text":"The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the Dichotomy Conjecture has been proved in 2017 independently by Bulatov and Zhuk. At about the same time, a vast generalisation of CSP, called promise CSP, has started to gain prominence. In this survey, we explain the importance of promise CSP and highlight many new very interesting features that the study of promise CSP has brought to light. The complexity classification quest for the promise CSP is wide open, and we argue that, despite the promise CSP being more general, this quest is rather more accessible to a wide range of researchers than the dichotomy-led study of the CSP has been."}],"type":"journal_article"},{"date_published":"2022-06-01T00:00:00Z","page":"225-240","article_type":"original","citation":{"chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591.","ieee":"O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591"},"publication":"Journal of Graph Algorithms and Applications","has_accepted_license":"1","article_processing_charge":"No","day":"01","scopus_import":"1","file":[{"file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","access_level":"open_access","creator":"dernst","file_size":694538,"content_type":"application/pdf","file_id":"11940","relation":"main_file","date_created":"2022-08-22T06:42:42Z","date_updated":"2022-08-22T06:42:42Z","success":1,"checksum":"dc6e255e3558faff924fd9e370886c11"}],"oa_version":"Published Version","intvolume":" 26","status":"public","title":"On compatible matchings","ddc":["000"],"_id":"11938","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","abstract":[{"text":"A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge.","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.7155/jgaa.00591","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF"},{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications"},{"call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Game Theory"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["2101.03928"]},"publication_identifier":{"issn":["1526-1719"]},"month":"06","volume":26,"date_updated":"2023-02-23T13:54:21Z","date_created":"2022-08-21T22:01:56Z","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"9296"}]},"author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"full_name":"Arroyo Guevara, Alan M","first_name":"Alan M","last_name":"Arroyo Guevara","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670"},{"full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová"},{"first_name":"Irene","last_name":"Parada","full_name":"Parada, Irene"},{"full_name":"Perz, Daniel","last_name":"Perz","first_name":"Daniel"},{"full_name":"Pilz, Alexander","last_name":"Pilz","first_name":"Alexander"},{"full_name":"Tkadlec, Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","first_name":"Josef","last_name":"Tkadlec"},{"full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber","first_name":"Birgit"}],"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"publisher":"Brown University","publication_status":"published","acknowledgement":"A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","year":"2022","ec_funded":1,"file_date_updated":"2022-08-22T06:42:42Z"},{"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-021-3"]},"month":"08","project":[{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"oa":1,"language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli"}],"doi":"10.15479/at:ista:11777","ec_funded":1,"file_date_updated":"2022-08-11T16:09:19Z","publisher":"Institute of Science and Technology","department":[{"_id":"GradSch"},{"_id":"UlWa"}],"publication_status":"published","year":"2022","date_created":"2022-08-10T15:51:19Z","date_updated":"2023-06-22T09:56:36Z","author":[{"full_name":"Wild, Pascal","id":"4C20D868-F248-11E8-B48F-1D18A9856A87","last_name":"Wild","first_name":"Pascal"}],"article_processing_charge":"No","has_accepted_license":"1","day":"11","page":"170","citation":{"chicago":"Wild, Pascal. “High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes.” Institute of Science and Technology, 2022. https://doi.org/10.15479/at:ista:11777.","short":"P. Wild, High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes, Institute of Science and Technology, 2022.","mla":"Wild, Pascal. High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes. Institute of Science and Technology, 2022, doi:10.15479/at:ista:11777.","apa":"Wild, P. (2022). High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology. https://doi.org/10.15479/at:ista:11777","ieee":"P. Wild, “High-dimensional expansion and crossing numbers of simplicial complexes,” Institute of Science and Technology, 2022.","ista":"Wild P. 2022. High-dimensional expansion and crossing numbers of simplicial complexes. Institute of Science and Technology.","ama":"Wild P. High-dimensional expansion and crossing numbers of simplicial complexes. 2022. doi:10.15479/at:ista:11777"},"date_published":"2022-08-11T00:00:00Z","alternative_title":["ISTA Thesis"],"type":"dissertation","abstract":[{"text":"In this dissertation we study coboundary expansion of simplicial complex with a view of giving geometric applications.\r\nOur main novel tool is an equivariant version of Gromov's celebrated Topological Overlap Theorem. The equivariant topological overlap theorem leads to various geometric applications including a quantitative non-embeddability result for sufficiently thick buildings (which partially resolves a conjecture of Tancer and Vorwerk) and an improved lower bound on the pair-crossing number of (bounded degree) expander graphs. Additionally, we will give new proofs for several known lower bounds for geometric problems such as the number of Tverberg partitions or the crossing number of complete bipartite graphs.\r\nFor the aforementioned applications one is naturally lead to study expansion properties of joins of simplicial complexes. In the presence of a special certificate for expansion (as it is the case, e.g., for spherical buildings), the join of two expanders is an expander. On the flip-side, we report quite some evidence that coboundary expansion exhibits very non-product-like behaviour under taking joins. For instance, we exhibit infinite families of graphs $(G_n)_{n\\in \\mathbb{N}}$ and $(H_n)_{n\\in\\mathbb{N}}$ whose join $G_n*H_n$ has expansion of lower order than the product of the expansion constant of the graphs. Moreover, we show an upper bound of $(d+1)/2^d$ on the normalized coboundary expansion constants for the complete multipartite complex $[n]^{*(d+1)}$ (under a mild divisibility condition on $n$).\r\nVia the probabilistic method the latter result extends to an upper bound of $(d+1)/2^d+\\varepsilon$ on the coboundary expansion constant of the spherical building associated with $\\mathrm{PGL}_{d+2}(\\mathbb{F}_q)$ for any $\\varepsilon>0$ and sufficiently large $q=q(\\varepsilon)$. This disproves a conjecture of Lubotzky, Meshulam and Mozes -- in a rather strong sense.\r\nBy improving on existing lower bounds we make further progress towards closing the gap between the known lower and upper bounds on the coboundary expansion constants of $[n]^{*(d+1)}$. The best improvements we achieve using computer-aided proofs and flag algebras. The exact value even for the complete $3$-partite $2$-dimensional complex $[n]^{*3}$ remains unknown but we are happy to conjecture a precise value for every $n$. %Moreover, we show that a previously shown lower bound on the expansion constant of the spherical building associated with $\\mathrm{PGL}_{2}(\\mathbb{F}_q)$ is not tight.\r\nIn a loosely structured, last chapter of this thesis we collect further smaller observations related to expansion. We point out a link between discrete Morse theory and a technique for showing coboundary expansion, elaborate a bit on the hardness of computing coboundary expansion constants, propose a new criterion for coboundary expansion (in a very dense setting) and give one way of making the folklore result that expansion of links is a necessary condition for a simplicial complex to be an expander precise.","lang":"eng"}],"ddc":["500","516","514"],"title":"High-dimensional expansion and crossing numbers of simplicial complexes","status":"public","_id":"11777","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Published Version","file":[{"description":"Code for computer-assisted proofs in Section 8.4.7 in Thesis","file_name":"flags.py","access_level":"open_access","file_size":16828,"content_type":"text/x-python","creator":"pwild","relation":"supplementary_material","file_id":"11780","date_updated":"2022-08-10T15:34:04Z","date_created":"2022-08-10T15:34:04Z","checksum":"f5f3af1fb7c8a24b71ddc88ad7f7c5b4"},{"checksum":"1f7c12dfe3bdaa9b147e4fbc3d34e3d5","date_created":"2022-08-10T15:34:10Z","date_updated":"2022-08-10T15:34:10Z","relation":"supplementary_material","file_id":"11781","file_size":12226,"content_type":"text/x-c++src","creator":"pwild","access_level":"open_access","description":"Code for proof of Lemma 8.20 in Thesis","file_name":"lowerbound.cpp"},{"file_size":3240,"content_type":"text/x-python","creator":"pwild","access_level":"open_access","file_name":"upperbound.py","description":"Code for proof of Proposition 7.9 in Thesis","checksum":"4cf81455c49e5dec3b9b2e3980137eeb","date_updated":"2022-08-10T15:34:17Z","date_created":"2022-08-10T15:34:17Z","relation":"supplementary_material","file_id":"11782"},{"checksum":"4e96575b10cbe4e0d0db2045b2847774","date_updated":"2022-08-11T16:08:33Z","date_created":"2022-08-11T16:08:33Z","relation":"main_file","file_id":"11809","title":"High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes","content_type":"application/pdf","file_size":5086282,"creator":"pwild","access_level":"open_access","file_name":"finalthesisPascalWildPDFA.pdf"},{"checksum":"92d94842a1fb6dca5808448137573b2e","date_updated":"2022-08-11T16:09:19Z","date_created":"2022-08-11T16:09:19Z","relation":"source_file","file_id":"11810","file_size":18150068,"content_type":"application/zip","creator":"pwild","access_level":"closed","file_name":"ThesisSubmission.zip"}]},{"date_published":"2022-12-01T00:00:00Z","page":"1317-1345","article_type":"original","citation":{"mla":"Kaluza, Vojtech, and Martin Tancer. “Even Maps, the Colin de Verdière Number and Representations of Graphs.” Combinatorica, vol. 42, Springer Nature, 2022, pp. 1317–45, doi:10.1007/s00493-021-4443-7.","short":"V. Kaluza, M. Tancer, Combinatorica 42 (2022) 1317–1345.","chicago":"Kaluza, Vojtech, and Martin Tancer. “Even Maps, the Colin de Verdière Number and Representations of Graphs.” Combinatorica. Springer Nature, 2022. https://doi.org/10.1007/s00493-021-4443-7.","ama":"Kaluza V, Tancer M. Even maps, the Colin de Verdière number and representations of graphs. Combinatorica. 2022;42:1317-1345. doi:10.1007/s00493-021-4443-7","ista":"Kaluza V, Tancer M. 2022. Even maps, the Colin de Verdière number and representations of graphs. Combinatorica. 42, 1317–1345.","ieee":"V. Kaluza and M. Tancer, “Even maps, the Colin de Verdière number and representations of graphs,” Combinatorica, vol. 42. Springer Nature, pp. 1317–1345, 2022.","apa":"Kaluza, V., & Tancer, M. (2022). Even maps, the Colin de Verdière number and representations of graphs. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-021-4443-7"},"publication":"Combinatorica","article_processing_charge":"No","day":"01","scopus_import":"1","oa_version":"Preprint","intvolume":" 42","title":"Even maps, the Colin de Verdière number and representations of graphs","status":"public","ddc":["514","516"],"_id":"10335","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"lang":"eng","text":"Van der Holst and Pendavingh introduced a graph parameter σ, which coincides with the more famous Colin de Verdière graph parameter μ for small values. However, the definition of a is much more geometric/topological directly reflecting embeddability properties of the graph. They proved μ(G) ≤ σ(G) + 2 and conjectured σ(G) ≤ σ(G) for any graph G. We confirm this conjecture. As far as we know, this is the first topological upper bound on σ(G) which is, in general, tight.\r\nEquality between μ and σ does not hold in general as van der Holst and Pendavingh showed that there is a graph G with μ(G) ≤ 18 and σ(G) ≥ 20. We show that the gap appears at much smaller values, namely, we exhibit a graph H for which μ(H) ≥ 7 and σ(H) ≥ 8. We also prove that, in general, the gap can be large: The incidence graphs Hq of finite projective planes of order q satisfy μ(Hq) ∈ O(q3/2) and σ(Hq) ≥ q2."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00493-021-4443-7","isi":1,"quality_controlled":"1","oa":1,"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1907.05055","open_access":"1"}],"external_id":{"arxiv":["1907.05055"],"isi":["000798210100003"]},"publication_identifier":{"issn":["0209-9683"]},"month":"12","volume":42,"date_updated":"2023-08-02T06:43:27Z","date_created":"2021-11-25T13:49:16Z","author":[{"orcid":"0000-0002-2512-8698","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","last_name":"Kaluza","first_name":"Vojtech","full_name":"Kaluza, Vojtech"},{"full_name":"Tancer, Martin","last_name":"Tancer","first_name":"Martin","orcid":"0000-0002-1191-6714","id":"38AC689C-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"UlWa"}],"publisher":"Springer Nature","publication_status":"published","year":"2022","acknowledgement":"V. K. gratefully acknowledges the support of Austrian Science Fund (FWF): P 30902-N35. This work was done mostly while he was employed at the University of Innsbruck. During the early stage of this research, V. K. was partially supported by Charles University project GAUK 926416. M. T. is supported by the grant no. 19-04113Y of the Czech Science Foundation(GA ˇCR) and partially supported by Charles University project UNCE/SCI/004."},{"abstract":[{"lang":"eng","text":"Let K be a convex body in Rn (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K∩h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p0 is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n≥2, there are always at least three distinct barycentric cuts through the point p0∈K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p0 are guaranteed if n≥3."}],"type":"journal_article","oa_version":"Preprint","status":"public","title":"Barycentric cuts through a convex body","intvolume":" 68","_id":"10776","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2022-12-01T00:00:00Z","article_type":"original","page":"1133-1154","publication":"Discrete and Computational Geometry","citation":{"ama":"Patakova Z, Tancer M, Wagner U. Barycentric cuts through a convex body. Discrete and Computational Geometry. 2022;68:1133-1154. doi:10.1007/s00454-021-00364-7","ista":"Patakova Z, Tancer M, Wagner U. 2022. Barycentric cuts through a convex body. Discrete and Computational Geometry. 68, 1133–1154.","ieee":"Z. Patakova, M. Tancer, and U. Wagner, “Barycentric cuts through a convex body,” Discrete and Computational Geometry, vol. 68. Springer Nature, pp. 1133–1154, 2022.","apa":"Patakova, Z., Tancer, M., & Wagner, U. (2022). Barycentric cuts through a convex body. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00364-7","mla":"Patakova, Zuzana, et al. “Barycentric Cuts through a Convex Body.” Discrete and Computational Geometry, vol. 68, Springer Nature, 2022, pp. 1133–54, doi:10.1007/s00454-021-00364-7.","short":"Z. Patakova, M. Tancer, U. Wagner, Discrete and Computational Geometry 68 (2022) 1133–1154.","chicago":"Patakova, Zuzana, Martin Tancer, and Uli Wagner. “Barycentric Cuts through a Convex Body.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-021-00364-7."},"date_created":"2022-02-20T23:01:35Z","date_updated":"2023-08-02T14:38:58Z","volume":68,"author":[{"id":"48B57058-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3975-1683","first_name":"Zuzana","last_name":"Patakova","full_name":"Patakova, Zuzana"},{"full_name":"Tancer, Martin","first_name":"Martin","last_name":"Tancer"},{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"acknowledgement":"The work by Zuzana Patáková has been partially supported by Charles University Research Center Program No. UNCE/SCI/022, and part of it was done during her research stay at IST Austria. The work by Martin Tancer is supported by the GAČR Grant 19-04113Y and by the Charles University Projects PRIMUS/17/SCI/3 and UNCE/SCI/004.","year":"2022","month":"12","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00454-021-00364-7","quality_controlled":"1","isi":1,"external_id":{"arxiv":["2003.13536"],"isi":["000750681500001"]},"main_file_link":[{"url":"https://arxiv.org/abs/2003.13536","open_access":"1"}],"oa":1},{"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2022-06-01T00:00:00Z","article_type":"original","citation":{"ieee":"G. Ivanov and M. Naszódi, “Functional John ellipsoids,” Journal of Functional Analysis, vol. 282, no. 11. Elsevier, 2022.","apa":"Ivanov, G., & Naszódi, M. (2022). Functional John ellipsoids. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109441","ista":"Ivanov G, Naszódi M. 2022. Functional John ellipsoids. Journal of Functional Analysis. 282(11), 109441.","ama":"Ivanov G, Naszódi M. Functional John ellipsoids. Journal of Functional Analysis. 2022;282(11). doi:10.1016/j.jfa.2022.109441","chicago":"Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109441.","short":"G. Ivanov, M. Naszódi, Journal of Functional Analysis 282 (2022).","mla":"Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” Journal of Functional Analysis, vol. 282, no. 11, 109441, Elsevier, 2022, doi:10.1016/j.jfa.2022.109441."},"publication":"Journal of Functional Analysis","issue":"11","abstract":[{"text":"We introduce a new way of representing logarithmically concave functions on Rd. It allows us to extend the notion of the largest volume ellipsoid contained in a convex body to the setting of logarithmically concave functions as follows. For every s>0, we define a class of non-negative functions on Rd derived from ellipsoids in Rd+1. For any log-concave function f on Rd , and any fixed s>0, we consider functions belonging to this class, and find the one with the largest integral under the condition that it is pointwise less than or equal to f, and we call it the John s-function of f. After establishing existence and uniqueness, we give a characterization of this function similar to the one given by John in his fundamental theorem. We find that John s-functions converge to characteristic functions of ellipsoids as s tends to zero and to Gaussian densities as s tends to infinity.\r\nAs an application, we prove a quantitative Helly type result: the integral of the pointwise minimum of any family of log-concave functions is at least a constant cd multiple of the integral of the pointwise minimum of a properly chosen subfamily of size 3d+2, where cd depends only on d.","lang":"eng"}],"type":"journal_article","file":[{"success":1,"checksum":"1cf185e264e04c87cb1ce67a00db88ab","date_updated":"2022-08-02T10:40:48Z","date_created":"2022-08-02T10:40:48Z","file_id":"11721","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":734482,"access_level":"open_access","file_name":"2022_JourFunctionalAnalysis_Ivanov.pdf"}],"oa_version":"Published Version","intvolume":" 282","status":"public","ddc":["510"],"title":"Functional John ellipsoids","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10887","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.1016/j.jfa.2022.109441","quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000781371300008"],"arxiv":["2006.09934"]},"oa":1,"file_date_updated":"2022-08-02T10:40:48Z","article_number":"109441","volume":282,"date_updated":"2023-08-02T14:51:11Z","date_created":"2022-03-20T23:01:38Z","author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","first_name":"Grigory","last_name":"Ivanov"},{"full_name":"Naszódi, Márton","last_name":"Naszódi","first_name":"Márton"}],"publisher":"Elsevier","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2022","acknowledgement":"G.I. was supported by the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported by the National Research, Development and Innovation Fund (NRDI) grants K119670 and KKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences and the New National Excellence Programme and the TKP2020-NKA-06 program provided by the NRDI. "},{"file":[{"creator":"dernst","content_type":"application/pdf","file_size":1747581,"file_name":"2022_DiscreteCompGeometry_Wagner.pdf","access_level":"open_access","date_updated":"2023-01-23T11:10:03Z","date_created":"2023-01-23T11:10:03Z","success":1,"checksum":"307e879d09e52eddf5b225d0aaa9213a","file_id":"12345","relation":"main_file"}],"oa_version":"Published Version","ddc":["510"],"status":"public","title":"Connectivity of triangulation flip graphs in the plane","intvolume":" 68","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12129","abstract":[{"text":"Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P′ of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar flip graph is (n−3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n−3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n−3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.","lang":"eng"}],"issue":"4","type":"journal_article","date_published":"2022-11-14T00:00:00Z","article_type":"original","page":"1227-1284","publication":"Discrete & Computational Geometry","citation":{"chicago":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” Discrete & Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00436-2.","mla":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane.” Discrete & Computational Geometry, vol. 68, no. 4, Springer Nature, 2022, pp. 1227–84, doi:10.1007/s00454-022-00436-2.","short":"U. Wagner, E. Welzl, Discrete & Computational Geometry 68 (2022) 1227–1284.","ista":"Wagner U, Welzl E. 2022. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 68(4), 1227–1284.","apa":"Wagner, U., & Welzl, E. (2022). Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00436-2","ieee":"U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane,” Discrete & Computational Geometry, vol. 68, no. 4. Springer Nature, pp. 1227–1284, 2022.","ama":"Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 2022;68(4):1227-1284. doi:10.1007/s00454-022-00436-2"},"day":"14","has_accepted_license":"1","article_processing_charge":"No","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"scopus_import":"1","date_created":"2023-01-12T12:02:28Z","date_updated":"2023-08-04T08:51:08Z","volume":68,"author":[{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"related_material":{"record":[{"id":"7807","relation":"earlier_version","status":"public"},{"id":"7990","relation":"earlier_version","status":"public"}]},"publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","acknowledgement":"This is a full and revised version of [38] (on partial triangulations) in Proceedings of the 36th Annual International Symposium on Computational Geometry (SoCG‘20) and of some of the results in [37] (on full triangulations) in Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA‘20).\r\nThis research started at the 11th Gremo’s Workshop on Open Problems (GWOP), Alp Sellamatt, Switzerland, June 24–28, 2013, motivated by a question posed by Filip Mori´c on full triangulations. Research was supported by the Swiss National Science Foundation within the collaborative DACH project Arrangements and Drawings as SNSF Project 200021E-171681, and by IST Austria and Berlin Free University during a sabbatical stay of the second author. We thank Michael Joswig, Jesús De Loera, and Francisco Santos for helpful discussions on the topics of this paper, and Daniel Bertschinger and Valentin Stoppiello for carefully reading earlier versions and for many helpful comments.\r\nOpen access funding provided by the Swiss Federal Institute of Technology Zürich","year":"2022","file_date_updated":"2023-01-23T11:10:03Z","language":[{"iso":"eng"}],"doi":"10.1007/s00454-022-00436-2","isi":1,"quality_controlled":"1","external_id":{"isi":["000883222200003"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"month":"11","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]}},{"scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Discrete and Computational Geometry","citation":{"chicago":"Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00412-w.","short":"R. Fulek, J. Kynčl, Discrete and Computational Geometry 68 (2022) 425–447.","mla":"Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” Discrete and Computational Geometry, vol. 68, Springer Nature, 2022, pp. 425–47, doi:10.1007/s00454-022-00412-w.","ieee":"R. Fulek and J. Kynčl, “The Z2-Genus of Kuratowski minors,” Discrete and Computational Geometry, vol. 68. Springer Nature, pp. 425–447, 2022.","apa":"Fulek, R., & Kynčl, J. (2022). The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00412-w","ista":"Fulek R, Kynčl J. 2022. The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. 68, 425–447.","ama":"Fulek R, Kynčl J. The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. 2022;68:425-447. doi:10.1007/s00454-022-00412-w"},"article_type":"original","page":"425-447","date_published":"2022-09-01T00:00:00Z","type":"journal_article","abstract":[{"text":"A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The Z2 -genus of a graph G is the minimum g such that G has an independently even drawing on the orientable surface of genus g. An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a minor a projective t×t grid or one of the following so-called t -Kuratowski graphs: K3,t, or t copies of K5 or K3,3 sharing at most two common vertices. We show that the Z2-genus of graphs in these families is unbounded in t; in fact, equal to their genus. Together, this implies that the genus of a graph is bounded from above by a function of its Z2-genus, solving a problem posed by Schaefer and Štefankovič, and giving an approximate version of the Hanani–Tutte theorem on orientable surfaces. We also obtain an analogous result for Euler genus and Euler Z2-genus of graphs.","lang":"eng"}],"_id":"11593","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The Z2-Genus of Kuratowski minors","status":"public","intvolume":" 68","oa_version":"Preprint","month":"09","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"oa":1,"external_id":{"arxiv":["1803.05085"],"isi":["000825014500001"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.05085"}],"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs","_id":"261FA626-B435-11E9-9278-68D0E5697425","grant_number":"M02281"}],"doi":"10.1007/s00454-022-00412-w","language":[{"iso":"eng"}],"acknowledgement":"We thank Zdeněk Dvořák, Xavier Goaoc, and Pavel Paták for helpful discussions. We also thank Bojan Mohar, Paul Seymour, Gelasio Salazar, Jim Geelen, and John Maharry for information about their unpublished results related to Conjecture 3.1. Finally we thank the reviewers for corrections and suggestions for improving the presentation.\r\nSupported by Austrian Science Fund (FWF): M2281-N35. Supported by project 19-04113Y of the Czech Science Foundation (GAČR), by the Czech-French collaboration project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM), and by Charles University project UNCE/SCI/004.","year":"2022","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","first_name":"Radoslav","last_name":"Fulek","full_name":"Fulek, Radoslav"},{"full_name":"Kynčl, Jan","first_name":"Jan","last_name":"Kynčl"}],"related_material":{"record":[{"id":"186","relation":"earlier_version","status":"public"}]},"date_updated":"2023-08-14T12:43:52Z","date_created":"2022-07-17T22:01:56Z","volume":68},{"oa_version":"Preprint","intvolume":" 13174","title":"Approximating the bundled crossing number","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"11185","abstract":[{"text":"Bundling crossings is a strategy which can enhance the readability of graph drawings. In this paper we consider bundlings for families of pseudosegments, i.e., simple curves such that any two have share at most one point at which they cross. Our main result is that there is a polynomial-time algorithm to compute an 8-approximation of the bundled crossing number of such instances (up to adding a term depending on the facial structure). This 8-approximation also holds for bundlings of good drawings of graphs. In the special case of circular drawings the approximation factor is 8 (no extra term), this improves upon the 10-approximation of Fink et al. [6]. We also show how to compute a 92-approximation when the intersection graph of the pseudosegments is bipartite.","lang":"eng"}],"type":"conference","date_published":"2022-03-16T00:00:00Z","page":"383-395","citation":{"ama":"Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. In: WALCOM 2022: Algorithms and Computation. Vol 13174. LNCS. Springer Nature; 2022:383-395. doi:10.1007/978-3-030-96731-4_31","ieee":"A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,” in WALCOM 2022: Algorithms and Computation, Jember, Indonesia, 2022, vol. 13174, pp. 383–395.","apa":"Arroyo Guevara, A. M., & Felsner, S. (2022). Approximating the bundled crossing number. In WALCOM 2022: Algorithms and Computation (Vol. 13174, pp. 383–395). Jember, Indonesia: Springer Nature. https://doi.org/10.1007/978-3-030-96731-4_31","ista":"Arroyo Guevara AM, Felsner S. 2022. Approximating the bundled crossing number. WALCOM 2022: Algorithms and Computation. WALCOM: Algorithms and ComputationLNCS vol. 13174, 383–395.","short":"A.M. Arroyo Guevara, S. Felsner, in:, WALCOM 2022: Algorithms and Computation, Springer Nature, 2022, pp. 383–395.","mla":"Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing Number.” WALCOM 2022: Algorithms and Computation, vol. 13174, Springer Nature, 2022, pp. 383–95, doi:10.1007/978-3-030-96731-4_31.","chicago":"Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled Crossing Number.” In WALCOM 2022: Algorithms and Computation, 13174:383–95. LNCS. Springer Nature, 2022. https://doi.org/10.1007/978-3-030-96731-4_31."},"publication":"WALCOM 2022: Algorithms and Computation","article_processing_charge":"No","day":"16","series_title":"LNCS","scopus_import":"1","volume":13174,"date_updated":"2023-09-25T10:56:10Z","date_created":"2022-04-17T22:01:47Z","related_material":{"record":[{"status":"public","relation":"later_version","id":"13969"}]},"author":[{"orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","first_name":"Alan M","full_name":"Arroyo Guevara, Alan M"},{"full_name":"Felsner, Stefan","last_name":"Felsner","first_name":"Stefan"}],"publisher":"Springer Nature","department":[{"_id":"UlWa"}],"publication_status":"published","acknowledgement":"This work was initiated during the Workshop on Geometric Graphs in November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during the workshop. The first author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska Curie grant agreement No 754411. The second author has been supported by the German Research Foundation DFG Project FE 340/12-1.","year":"2022","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-96731-4_31","conference":{"name":"WALCOM: Algorithms and Computation","end_date":"2022-03-26","location":"Jember, Indonesia","start_date":"2022-03-24"},"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2109.14892"}],"external_id":{"arxiv":["2109.14892"]},"publication_identifier":{"isbn":["9783030967307"],"eissn":["1611-3349"],"issn":["0302-9743"]},"month":"03"},{"type":"journal_article","abstract":[{"lang":"eng","text":"Expander graphs (sparse but highly connected graphs) have, since their inception, been the source of deep links between Mathematics and Computer Science as well as applications to other areas. In recent years, a fascinating theory of high-dimensional expanders has begun to emerge, which is still in a formative stage but has nonetheless already lead to a number of striking results. Unlike for graphs, in higher dimensions there is a rich array of non-equivalent notions of expansion (coboundary expansion, cosystolic expansion, topological expansion, spectral expansion, etc.), with differents strengths and applications. In this talk, we will survey this landscape of high-dimensional expansion, with a focus on two main results. First, we will present Gromov’s Topological Overlap Theorem, which asserts that coboundary expansion (a quantitative version of vanishing mod 2 cohomology) implies topological expansion (roughly, the property that for every map from a simplicial complex to a manifold of the same dimension, the images of a positive fraction of the simplices have a point in common). Second, we will outline a construction of bounded degree 2-dimensional topological expanders, due to Kaufman, Kazhdan, and Lubotzky."}],"_id":"14381","year":"2022","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Societe Mathematique de France","intvolume":" 438","department":[{"_id":"UlWa"}],"title":"High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others)","status":"public","publication_status":"published","author":[{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli"}],"volume":438,"oa_version":"None","date_created":"2023-10-01T22:01:14Z","date_updated":"2023-10-03T08:04:03Z","scopus_import":"1","publication_identifier":{"issn":["0037-9484"],"eissn":["2102-622X"]},"article_processing_charge":"No","day":"01","month":"01","citation":{"chicago":"Wagner, Uli. “High-Dimensional Expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and Others).” Bulletin de La Societe Mathematique de France. Societe Mathematique de France, 2022. https://doi.org/10.24033/ast.1188.","mla":"Wagner, Uli. “High-Dimensional Expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and Others).” Bulletin de La Societe Mathematique de France, vol. 438, Societe Mathematique de France, 2022, pp. 281–94, doi:10.24033/ast.1188.","short":"U. Wagner, Bulletin de La Societe Mathematique de France 438 (2022) 281–294.","ista":"Wagner U. 2022. High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others). Bulletin de la Societe Mathematique de France. 438, 281–294.","ieee":"U. Wagner, “High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others),” Bulletin de la Societe Mathematique de France, vol. 438. Societe Mathematique de France, pp. 281–294, 2022.","apa":"Wagner, U. (2022). High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others). Bulletin de La Societe Mathematique de France. Societe Mathematique de France. https://doi.org/10.24033/ast.1188","ama":"Wagner U. High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others). Bulletin de la Societe Mathematique de France. 2022;438:281-294. doi:10.24033/ast.1188"},"publication":"Bulletin de la Societe Mathematique de France","page":"281-294","article_type":"original","quality_controlled":"1","doi":"10.24033/ast.1188","date_published":"2022-01-01T00:00:00Z","language":[{"iso":"eng"}]},{"article_type":"original","page":"951-957","publication":"SIAM Journal on Discrete Mathematics","citation":{"short":"G. Ivanov, M. Naszodi, SIAM Journal on Discrete Mathematics 36 (2022) 951–957.","mla":"Ivanov, Grigory, and Marton Naszodi. “A Quantitative Helly-Type Theorem: Containment in a Homothet.” SIAM Journal on Discrete Mathematics, vol. 36, no. 2, Society for Industrial and Applied Mathematics, 2022, pp. 951–57, doi:10.1137/21M1403308.","chicago":"Ivanov, Grigory, and Marton Naszodi. “A Quantitative Helly-Type Theorem: Containment in a Homothet.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21M1403308.","ama":"Ivanov G, Naszodi M. A quantitative Helly-type theorem: Containment in a homothet. SIAM Journal on Discrete Mathematics. 2022;36(2):951-957. doi:10.1137/21M1403308","ieee":"G. Ivanov and M. Naszodi, “A quantitative Helly-type theorem: Containment in a homothet,” SIAM Journal on Discrete Mathematics, vol. 36, no. 2. Society for Industrial and Applied Mathematics, pp. 951–957, 2022.","apa":"Ivanov, G., & Naszodi, M. (2022). A quantitative Helly-type theorem: Containment in a homothet. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1403308","ista":"Ivanov G, Naszodi M. 2022. A quantitative Helly-type theorem: Containment in a homothet. SIAM Journal on Discrete Mathematics. 36(2), 951–957."},"date_published":"2022-04-11T00:00:00Z","scopus_import":"1","day":"11","article_processing_charge":"No","status":"public","title":"A quantitative Helly-type theorem: Containment in a homothet","intvolume":" 36","_id":"11435","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"We introduce a new variant of quantitative Helly-type theorems: the minimal homothetic distance of the intersection of a family of convex sets to the intersection of a subfamily of a fixed size. As an application, we establish the following quantitative Helly-type result for the diameter. If $K$ is the intersection of finitely many convex bodies in $\\mathbb{R}^d$, then one can select $2d$ of these bodies whose intersection is of diameter at most $(2d)^3{diam}(K)$. The best previously known estimate, due to Brazitikos [Bull. Hellenic Math. Soc., 62 (2018), pp. 19--25], is $c d^{11/2}$. Moreover, we confirm that the multiplicative factor $c d^{1/2}$ conjectured by Bárány, Katchalski, and Pach [Proc. Amer. Math. Soc., 86 (1982), pp. 109--114] cannot be improved. The bounds above follow from our key result that concerns sparse approximation of a convex polytope by the convex hull of a well-chosen subset of its vertices: Assume that $Q \\subset {\\mathbb R}^d$ is a polytope whose centroid is the origin. Then there exist at most 2d vertices of $Q$ whose convex hull $Q^{\\prime \\prime}$ satisfies $Q \\subset - 8d^3 Q^{\\prime \\prime}.$","lang":"eng"}],"issue":"2","isi":1,"quality_controlled":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.04122","open_access":"1"}],"oa":1,"external_id":{"arxiv":["2103.04122"],"isi":["000793158200002"]},"language":[{"iso":"eng"}],"doi":"10.1137/21M1403308","month":"04","publication_identifier":{"issn":["0895-4801"]},"publication_status":"published","publisher":"Society for Industrial and Applied Mathematics","department":[{"_id":"UlWa"}],"acknowledgement":"G.I. acknowledges the financial support from the Ministry of Educational and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported by the National Research, Development and Innovation Fund (NRDI) grants K119670 and\r\nKKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences and the New National Excellence Programme and the TKP2020-NKA-06 program provided by the NRDI.","year":"2022","date_updated":"2023-10-18T06:58:03Z","date_created":"2022-06-05T22:01:50Z","volume":36,"author":[{"id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov","first_name":"Grigory","full_name":"Ivanov, Grigory"},{"last_name":"Naszodi","first_name":"Marton","full_name":"Naszodi, Marton"}]},{"oa_version":"Preprint","_id":"9296","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","intvolume":" 12635","status":"public","title":"On compatible matchings","abstract":[{"lang":"eng","text":" matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge."}],"type":"conference","alternative_title":["LNCS"],"date_published":"2021-02-16T00:00:00Z","citation":{"ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18","ieee":"O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18."},"publication":"15th International Conference on Algorithms and Computation","page":"221-233","article_processing_charge":"No","day":"16","scopus_import":"1","related_material":{"record":[{"status":"public","relation":"later_version","id":"11938"}]},"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","first_name":"Alan M","full_name":"Arroyo Guevara, Alan M"},{"last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"first_name":"Josef","last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"volume":12635,"date_updated":"2023-02-21T16:33:44Z","date_created":"2021-03-28T22:01:41Z","year":"2021","acknowledgement":"A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","publisher":"Springer Nature","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"publication_status":"published","ec_funded":1,"doi":"10.1007/978-3-030-68211-8_18","conference":{"name":"WALCOM: Algorithms and Computation","location":"Yangon, Myanmar","start_date":"2021-02-28","end_date":"2021-03-02"},"language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["2101.03928"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.03928"}],"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"},{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307"},{"_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","call_identifier":"FWF"}],"quality_controlled":"1","publication_identifier":{"issn":["03029743"],"eissn":["16113349"],"isbn":["9783030682101"]},"month":"02"},{"isi":1,"quality_controlled":"1","external_id":{"arxiv":["1912.08561"],"isi":["000607265100001"]},"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1112/blms.12449","publication_identifier":{"issn":["00246093"],"eissn":["14692120"]},"month":"04","publisher":"London Mathematical Society","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2021","acknowledgement":"I wish to thank Imre Bárány for bringing the problem to my attention. I am grateful to Marton Naszódi and Igor Tsiutsiurupa for useful remarks and help with the text.\r\nThe author acknowledges the financial support from the Ministry of Educational and Science of the Russian Federation in the framework of MegaGrant no 075‐15‐2019‐1926.","volume":53,"date_updated":"2023-08-07T13:35:20Z","date_created":"2021-01-24T23:01:08Z","author":[{"full_name":"Ivanov, Grigory","first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"}],"file_date_updated":"2021-08-06T09:59:45Z","page":"631-641","article_type":"original","citation":{"ama":"Ivanov G. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. 2021;53(2):631-641. doi:10.1112/blms.12449","apa":"Ivanov, G. (2021). No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12449","ieee":"G. Ivanov, “No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p,” Bulletin of the London Mathematical Society, vol. 53, no. 2. London Mathematical Society, pp. 631–641, 2021.","ista":"Ivanov G. 2021. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. 53(2), 631–641.","short":"G. Ivanov, Bulletin of the London Mathematical Society 53 (2021) 631–641.","mla":"Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” Bulletin of the London Mathematical Society, vol. 53, no. 2, London Mathematical Society, 2021, pp. 631–41, doi:10.1112/blms.12449.","chicago":"Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” Bulletin of the London Mathematical Society. London Mathematical Society, 2021. https://doi.org/10.1112/blms.12449."},"publication":"Bulletin of the London Mathematical Society","date_published":"2021-04-01T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","intvolume":" 53","title":"No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p","status":"public","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9037","oa_version":"Published Version","file":[{"file_size":194550,"content_type":"application/pdf","creator":"kschuh","access_level":"open_access","file_name":"2021_BLMS_Ivanov.pdf","checksum":"e6ceaa6470d835eb4c211cbdd38fdfd1","success":1,"date_created":"2021-08-06T09:59:45Z","date_updated":"2021-08-06T09:59:45Z","relation":"main_file","file_id":"9796"}],"type":"journal_article","issue":"2","abstract":[{"lang":"eng","text":"We continue our study of ‘no‐dimension’ analogues of basic theorems in combinatorial and convex geometry in Banach spaces. We generalize some results of the paper (Adiprasito, Bárány and Mustafa, ‘Theorems of Carathéodory, Helly, and Tverberg without dimension’, Proceedings of the Thirtieth Annual ACM‐SIAM Symposium on Discrete Algorithms (Society for Industrial and Applied Mathematics, San Diego, California, 2019) 2350–2360) and prove no‐dimension versions of the colored Tverberg theorem, the selection lemma and the weak 𝜀 ‐net theorem in Banach spaces of type 𝑝>1 . To prove these results, we use the original ideas of Adiprasito, Bárány and Mustafa for the Euclidean case, our no‐dimension version of the Radon theorem and slightly modified version of the celebrated Maurey lemma."}]},{"language":[{"iso":"eng"}],"doi":"10.1016/j.disc.2021.112312","quality_controlled":"1","isi":1,"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1808.09165","open_access":"1"}],"external_id":{"arxiv":["1808.09165"],"isi":["000633365200001"]},"month":"05","publication_identifier":{"issn":["0012365X"]},"date_updated":"2023-08-07T13:40:37Z","date_created":"2021-02-07T23:01:12Z","volume":344,"author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","first_name":"Grigory","last_name":"Ivanov"}],"publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Elsevier","year":"2021","acknowledgement":"Research was supported by the Russian Foundation for Basic Research, project 18-01-00036A (Theorems 1.5 and 5.3) and by the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926 (Theorems 1.2 and 7.3).","article_number":"112312","date_published":"2021-05-01T00:00:00Z","article_type":"original","publication":"Discrete Mathematics","citation":{"chicago":"Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” Discrete Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.disc.2021.112312.","short":"G. Ivanov, Discrete Mathematics 344 (2021).","mla":"Ivanov, Grigory. “On the Volume of Projections of the Cross-Polytope.” Discrete Mathematics, vol. 344, no. 5, 112312, Elsevier, 2021, doi:10.1016/j.disc.2021.112312.","apa":"Ivanov, G. (2021). On the volume of projections of the cross-polytope. Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.disc.2021.112312","ieee":"G. Ivanov, “On the volume of projections of the cross-polytope,” Discrete Mathematics, vol. 344, no. 5. Elsevier, 2021.","ista":"Ivanov G. 2021. On the volume of projections of the cross-polytope. Discrete Mathematics. 344(5), 112312.","ama":"Ivanov G. On the volume of projections of the cross-polytope. Discrete Mathematics. 2021;344(5). doi:10.1016/j.disc.2021.112312"},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","status":"public","title":"On the volume of projections of the cross-polytope","intvolume":" 344","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9098","abstract":[{"text":"We study properties of the volume of projections of the n-dimensional\r\ncross-polytope $\\crosp^n = \\{ x \\in \\R^n \\mid |x_1| + \\dots + |x_n| \\leqslant 1\\}.$ We prove that the projection of $\\crosp^n$ onto a k-dimensional coordinate subspace has the maximum possible volume for k=2 and for k=3.\r\nWe obtain the exact lower bound on the volume of such a projection onto a two-dimensional plane. Also, we show that there exist local maxima which are not global ones for the volume of a projection of $\\crosp^n$ onto a k-dimensional subspace for any n>k⩾2.","lang":"eng"}],"issue":"5","type":"journal_article"},{"abstract":[{"lang":"eng","text":"Hill's Conjecture states that the crossing number cr(𝐾𝑛) of the complete graph 𝐾𝑛 in the plane (equivalently, the sphere) is 14⌊𝑛2⌋⌊𝑛−12⌋⌊𝑛−22⌋⌊𝑛−32⌋=𝑛4/64+𝑂(𝑛3) . Moon proved that the expected number of crossings in a spherical drawing in which the points are randomly distributed and joined by geodesics is precisely 𝑛4/64+𝑂(𝑛3) , thus matching asymptotically the conjectured value of cr(𝐾𝑛) . Let cr𝑃(𝐺) denote the crossing number of a graph 𝐺 in the projective plane. Recently, Elkies proved that the expected number of crossings in a naturally defined random projective plane drawing of 𝐾𝑛 is (𝑛4/8𝜋2)+𝑂(𝑛3) . In analogy with the relation of Moon's result to Hill's conjecture, Elkies asked if lim𝑛→∞ cr𝑃(𝐾𝑛)/𝑛4=1/8𝜋2 . We construct drawings of 𝐾𝑛 in the projective plane that disprove this."}],"issue":"3","type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9295","status":"public","title":"Drawings of complete graphs in the projective plane","intvolume":" 97","day":"23","article_processing_charge":"No","scopus_import":"1","date_published":"2021-03-23T00:00:00Z","publication":"Journal of Graph Theory","citation":{"ieee":"A. M. Arroyo Guevara, D. Mcquillan, R. B. Richter, G. Salazar, and M. Sullivan, “Drawings of complete graphs in the projective plane,” Journal of Graph Theory, vol. 97, no. 3. Wiley, pp. 426–440, 2021.","apa":"Arroyo Guevara, A. M., Mcquillan, D., Richter, R. B., Salazar, G., & Sullivan, M. (2021). Drawings of complete graphs in the projective plane. Journal of Graph Theory. Wiley. https://doi.org/10.1002/jgt.22665","ista":"Arroyo Guevara AM, Mcquillan D, Richter RB, Salazar G, Sullivan M. 2021. Drawings of complete graphs in the projective plane. Journal of Graph Theory. 97(3), 426–440.","ama":"Arroyo Guevara AM, Mcquillan D, Richter RB, Salazar G, Sullivan M. Drawings of complete graphs in the projective plane. Journal of Graph Theory. 2021;97(3):426-440. doi:10.1002/jgt.22665","chicago":"Arroyo Guevara, Alan M, Dan Mcquillan, R. Bruce Richter, Gelasio Salazar, and Matthew Sullivan. “Drawings of Complete Graphs in the Projective Plane.” Journal of Graph Theory. Wiley, 2021. https://doi.org/10.1002/jgt.22665.","short":"A.M. Arroyo Guevara, D. Mcquillan, R.B. Richter, G. Salazar, M. Sullivan, Journal of Graph Theory 97 (2021) 426–440.","mla":"Arroyo Guevara, Alan M., et al. “Drawings of Complete Graphs in the Projective Plane.” Journal of Graph Theory, vol. 97, no. 3, Wiley, 2021, pp. 426–40, doi:10.1002/jgt.22665."},"article_type":"original","page":"426-440","ec_funded":1,"author":[{"full_name":"Arroyo Guevara, Alan M","orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","first_name":"Alan M"},{"first_name":"Dan","last_name":"Mcquillan","full_name":"Mcquillan, Dan"},{"full_name":"Richter, R. Bruce","first_name":"R. Bruce","last_name":"Richter"},{"full_name":"Salazar, Gelasio","last_name":"Salazar","first_name":"Gelasio"},{"last_name":"Sullivan","first_name":"Matthew","full_name":"Sullivan, Matthew"}],"date_created":"2021-03-28T22:01:41Z","date_updated":"2023-08-07T14:26:15Z","volume":97,"acknowledgement":"We thank two reviewers for their corrections and suggestions on the original version of this\r\npaper. This project has received funding from NSERC Grant 50503-10940-500 and from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie grant agreement No 754411, IST, Klosterneuburg, Austria.","year":"2021","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Wiley","month":"03","publication_identifier":{"eissn":["1097-0118"],"issn":["0364-9024"]},"doi":"10.1002/jgt.22665","language":[{"iso":"eng"}],"external_id":{"isi":["000631693200001"],"arxiv":["2002.02287"]},"main_file_link":[{"url":"https://arxiv.org/abs/2002.02287","open_access":"1"}],"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}]},{"ec_funded":1,"year":"2021","department":[{"_id":"UlWa"}],"publisher":"Society for Industrial and Applied Mathematics","publication_status":"published","author":[{"full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","first_name":"Alan M","last_name":"Arroyo Guevara"},{"last_name":"Richter","first_name":"R. Bruce","full_name":"Richter, R. Bruce"},{"full_name":"Sunohara, Matthew","first_name":"Matthew","last_name":"Sunohara"}],"volume":35,"date_updated":"2023-08-08T13:58:12Z","date_created":"2021-06-06T22:01:30Z","publication_identifier":{"issn":["08954801"]},"month":"05","main_file_link":[{"url":"https://arxiv.org/abs/2001.06053","open_access":"1"}],"oa":1,"external_id":{"arxiv":["2001.06053"],"isi":["000674142200022"]},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","isi":1,"doi":"10.1137/20M1313234","language":[{"iso":"eng"}],"type":"journal_article","issue":"2","abstract":[{"lang":"eng","text":"Motivated by the successful application of geometry to proving the Harary--Hill conjecture for “pseudolinear” drawings of $K_n$, we introduce “pseudospherical” drawings of graphs. A spherical drawing of a graph $G$ is a drawing in the unit sphere $\\mathbb{S}^2$ in which the vertices of $G$ are represented as points---no three on a great circle---and the edges of $G$ are shortest-arcs in $\\mathbb{S}^2$ connecting pairs of vertices. Such a drawing has three properties: (1) every edge $e$ is contained in a simple closed curve $\\gamma_e$ such that the only vertices in $\\gamma_e$ are the ends of $e$; (2) if $e\\ne f$, then $\\gamma_e\\cap\\gamma_f$ has precisely two crossings; and (3) if $e\\ne f$, then $e$ intersects $\\gamma_f$ at most once, in either a crossing or an end of $e$. We use properties (1)--(3) to define a pseudospherical drawing of $G$. Our main result is that for the complete graph, properties (1)--(3) are equivalent to the same three properties but with “precisely two crossings” in (2) replaced by “at most two crossings.” The proof requires a result in the geometric transversal theory of arrangements of pseudocircles. This is proved using the surprising result that the absence of special arcs (coherent spirals) in an arrangement of simple closed curves characterizes the fact that any two curves in the arrangement have at most two crossings. Our studies provide the necessary ideas for exhibiting a drawing of $K_{10}$ that has no extension to an arrangement of pseudocircles and a drawing of $K_9$ that does extend to an arrangement of pseudocircles, but no such extension has all pairs of pseudocircles crossing twice.\r\n"}],"_id":"9468","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 35","status":"public","title":"Extending drawings of complete graphs into arrangements of pseudocircles","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"20","citation":{"ista":"Arroyo Guevara AM, Richter RB, Sunohara M. 2021. Extending drawings of complete graphs into arrangements of pseudocircles. SIAM Journal on Discrete Mathematics. 35(2), 1050–1076.","ieee":"A. M. Arroyo Guevara, R. B. Richter, and M. Sunohara, “Extending drawings of complete graphs into arrangements of pseudocircles,” SIAM Journal on Discrete Mathematics, vol. 35, no. 2. Society for Industrial and Applied Mathematics, pp. 1050–1076, 2021.","apa":"Arroyo Guevara, A. M., Richter, R. B., & Sunohara, M. (2021). Extending drawings of complete graphs into arrangements of pseudocircles. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1313234","ama":"Arroyo Guevara AM, Richter RB, Sunohara M. Extending drawings of complete graphs into arrangements of pseudocircles. SIAM Journal on Discrete Mathematics. 2021;35(2):1050-1076. doi:10.1137/20M1313234","chicago":"Arroyo Guevara, Alan M, R. Bruce Richter, and Matthew Sunohara. “Extending Drawings of Complete Graphs into Arrangements of Pseudocircles.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/20M1313234.","mla":"Arroyo Guevara, Alan M., et al. “Extending Drawings of Complete Graphs into Arrangements of Pseudocircles.” SIAM Journal on Discrete Mathematics, vol. 35, no. 2, Society for Industrial and Applied Mathematics, 2021, pp. 1050–76, doi:10.1137/20M1313234.","short":"A.M. Arroyo Guevara, R.B. Richter, M. Sunohara, SIAM Journal on Discrete Mathematics 35 (2021) 1050–1076."},"publication":"SIAM Journal on Discrete Mathematics","page":"1050-1076","article_type":"original","date_published":"2021-05-20T00:00:00Z"},{"external_id":{"arxiv":["2008.09543"],"isi":["000656507500001"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.09543"}],"oa":1,"quality_controlled":"1","isi":1,"doi":"10.1007/s12220-021-00691-4","language":[{"iso":"eng"}],"month":"05","publication_identifier":{"issn":["1050-6926"],"eissn":["1559-002X"]},"year":"2021","acknowledgement":"The authors acknowledge the support of the grant of the Russian Government N 075-15-2019-1926.","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer","author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov","first_name":"Grigory"},{"first_name":"Igor","last_name":"Tsiutsiurupa","full_name":"Tsiutsiurupa, Igor"}],"date_updated":"2023-08-08T14:04:49Z","date_created":"2021-06-13T22:01:32Z","volume":31,"publication":"Journal of Geometric Analysis","citation":{"apa":"Ivanov, G., & Tsiutsiurupa, I. (2021). Functional Löwner ellipsoids. Journal of Geometric Analysis. Springer. https://doi.org/10.1007/s12220-021-00691-4","ieee":"G. Ivanov and I. Tsiutsiurupa, “Functional Löwner ellipsoids,” Journal of Geometric Analysis, vol. 31. Springer, pp. 11493–11528, 2021.","ista":"Ivanov G, Tsiutsiurupa I. 2021. Functional Löwner ellipsoids. Journal of Geometric Analysis. 31, 11493–11528.","ama":"Ivanov G, Tsiutsiurupa I. Functional Löwner ellipsoids. Journal of Geometric Analysis. 2021;31:11493-11528. doi:10.1007/s12220-021-00691-4","chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “Functional Löwner Ellipsoids.” Journal of Geometric Analysis. Springer, 2021. https://doi.org/10.1007/s12220-021-00691-4.","short":"G. Ivanov, I. Tsiutsiurupa, Journal of Geometric Analysis 31 (2021) 11493–11528.","mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “Functional Löwner Ellipsoids.” Journal of Geometric Analysis, vol. 31, Springer, 2021, pp. 11493–528, doi:10.1007/s12220-021-00691-4."},"article_type":"original","page":"11493-11528","date_published":"2021-05-31T00:00:00Z","scopus_import":"1","day":"31","article_processing_charge":"No","_id":"9548","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"Functional Löwner ellipsoids","intvolume":" 31","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"We extend the notion of the minimal volume ellipsoid containing a convex body in Rd to the setting of logarithmically concave functions. We consider a vast class of logarithmically concave functions whose superlevel sets are concentric ellipsoids. For a fixed function from this class, we consider the set of all its “affine” positions. For any log-concave function f on Rd, we consider functions belonging to this set of “affine” positions, and find the one with the minimal integral under the condition that it is pointwise greater than or equal to f. We study the properties of existence and uniqueness of the solution to this problem. For any s∈[0,+∞), we consider the construction dual to the recently defined John s-function (Ivanov and Naszódi in Functional John ellipsoids. arXiv preprint: arXiv:2006.09934, 2020). We prove that such a construction determines a unique function and call it the Löwner s-function of f. We study the Löwner s-functions as s tends to zero and to infinity. Finally, extending the notion of the outer volume ratio, we define the outer integral ratio of a log-concave function and give an asymptotically tight bound on it."}]},{"abstract":[{"text":"In this article we study some geometric properties of proximally smooth sets. First, we introduce a modification of the metric projection and prove its existence. Then we provide an algorithm for constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space, with the moduli of smoothness and convexity of power type. Our algorithm returns a reasonably short curve between two sufficiently close points of a proximally smooth set, is iterative and uses our modification of the metric projection. We estimate the length of the constructed curve and its deviation from the segment with the same endpoints. These estimates coincide up to a constant factor with those for the geodesics in a proximally smooth set in a Hilbert space.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","_id":"10181","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Rectifiable curves in proximally smooth sets","status":"public","article_processing_charge":"No","day":"09","scopus_import":"1","date_published":"2021-10-09T00:00:00Z","citation":{"chicago":"Ivanov, Grigory, and Mariana S. Lopushanski. “Rectifiable Curves in Proximally Smooth Sets.” Set-Valued and Variational Analysis. Springer Nature, 2021. https://doi.org/10.1007/s11228-021-00612-1.","short":"G. Ivanov, M.S. Lopushanski, Set-Valued and Variational Analysis (2021).","mla":"Ivanov, Grigory, and Mariana S. Lopushanski. “Rectifiable Curves in Proximally Smooth Sets.” Set-Valued and Variational Analysis, Springer Nature, 2021, doi:10.1007/s11228-021-00612-1.","ieee":"G. Ivanov and M. S. Lopushanski, “Rectifiable curves in proximally smooth sets,” Set-Valued and Variational Analysis. Springer Nature, 2021.","apa":"Ivanov, G., & Lopushanski, M. S. (2021). Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis. Springer Nature. https://doi.org/10.1007/s11228-021-00612-1","ista":"Ivanov G, Lopushanski MS. 2021. Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis.","ama":"Ivanov G, Lopushanski MS. Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis. 2021. doi:10.1007/s11228-021-00612-1"},"publication":"Set-Valued and Variational Analysis","article_type":"original","author":[{"last_name":"Ivanov","first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"},{"last_name":"Lopushanski","first_name":"Mariana S.","full_name":"Lopushanski, Mariana S."}],"date_updated":"2023-08-14T08:11:38Z","date_created":"2021-10-24T22:01:35Z","year":"2021","acknowledgement":"Theorem 2 was obtained at Steklov Mathematical Institute RAS and supported by Russian Science Foundation, grant N 19-11-00087.","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"publication_status":"published","publication_identifier":{"issn":["0927-6947"],"eissn":["1877-0541"]},"month":"10","doi":"10.1007/s11228-021-00612-1","language":[{"iso":"eng"}],"oa":1,"external_id":{"isi":["000705774800001"],"arxiv":["2012.10691"]},"main_file_link":[{"url":"https://arxiv.org/abs/2012.10691","open_access":"1"}],"isi":1,"quality_controlled":"1"},{"oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10220","intvolume":" 245","title":"Eliminating higher-multiplicity intersections. III. Codimension 2","status":"public","abstract":[{"text":"We study conditions under which a finite simplicial complex K can be mapped to ℝd without higher-multiplicity intersections. An almost r-embedding is a map f: K → ℝd such that the images of any r pairwise disjoint simplices of K do not have a common point. We show that if r is not a prime power and d ≥ 2r + 1, then there is a counterexample to the topological Tverberg conjecture, i.e., there is an almost r-embedding of the (d +1)(r − 1)-simplex in ℝd. This improves on previous constructions of counterexamples (for d ≥ 3r) based on a series of papers by M. Özaydin, M. Gromov, P. Blagojević, F. Frick, G. Ziegler, and the second and fourth present authors.\r\n\r\nThe counterexamples are obtained by proving the following algebraic criterion in codimension 2: If r ≥ 3 and if K is a finite 2(r − 1)-complex, then there exists an almost r-embedding K → ℝ2r if and only if there exists a general position PL map f: K → ℝ2r such that the algebraic intersection number of the f-images of any r pairwise disjoint simplices of K is zero. This result can be restated in terms of a cohomological obstruction and extends an analogous codimension 3 criterion by the second and fourth authors. As another application, we classify ornaments f: S3 ⊔ S3 ⊔ S3 → ℝ5 up to ornament concordance.\r\n\r\nIt follows from work of M. Freedman, V. Krushkal and P. Teichner that the analogous criterion for r = 2 is false. We prove a lemma on singular higher-dimensional Borromean rings, yielding an elementary proof of the counterexample.","lang":"eng"}],"type":"journal_article","date_published":"2021-10-30T00:00:00Z","citation":{"ama":"Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. 2021;245:501–534. doi:10.1007/s11856-021-2216-z","ieee":"S. Avvakumov, I. Mabillard, A. B. Skopenkov, and U. Wagner, “Eliminating higher-multiplicity intersections. III. Codimension 2,” Israel Journal of Mathematics, vol. 245. Springer Nature, pp. 501–534, 2021.","apa":"Avvakumov, S., Mabillard, I., Skopenkov, A. B., & Wagner, U. (2021). Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-021-2216-z","ista":"Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. 2021. Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. 245, 501–534.","short":"S. Avvakumov, I. Mabillard, A.B. Skopenkov, U. Wagner, Israel Journal of Mathematics 245 (2021) 501–534.","mla":"Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections. III. Codimension 2.” Israel Journal of Mathematics, vol. 245, Springer Nature, 2021, pp. 501–534, doi:10.1007/s11856-021-2216-z.","chicago":"Avvakumov, Sergey, Isaac Mabillard, Arkadiy B. Skopenkov, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections. III. Codimension 2.” Israel Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s11856-021-2216-z."},"publication":"Israel Journal of Mathematics","page":"501–534 ","article_type":"original","article_processing_charge":"No","day":"30","scopus_import":"1","related_material":{"record":[{"id":"8183","status":"public","relation":"earlier_version"},{"relation":"earlier_version","status":"public","id":"9308"}]},"author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","last_name":"Avvakumov","full_name":"Avvakumov, Sergey"},{"first_name":"Isaac","last_name":"Mabillard","id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","full_name":"Mabillard, Isaac"},{"last_name":"Skopenkov","first_name":"Arkadiy B.","full_name":"Skopenkov, Arkadiy B."},{"full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"}],"volume":245,"date_updated":"2023-08-14T11:43:55Z","date_created":"2021-11-07T23:01:24Z","acknowledgement":"Research supported by the Swiss National Science Foundation (Project SNSF-PP00P2-138948), by the Austrian Science Fund (FWF Project P31312-N35), by the Russian Foundation for Basic Research (Grants No. 15-01-06302 and 19-01-00169), by a Simons-IUM Fellowship, and by the D. Zimin Dynasty Foundation Grant. We would like to thank E. Alkin, A. Klyachko, V. Krushkal, S. Melikhov, M. Tancer, P. Teichner and anonymous referees for helpful comments and discussions.","year":"2021","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"publication_status":"published","doi":"10.1007/s11856-021-2216-z","language":[{"iso":"eng"}],"external_id":{"arxiv":["1511.03501"],"isi":["000712942100013"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1511.03501"}],"oa":1,"project":[{"_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312","name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF"}],"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["0021-2172"],"eissn":["1565-8511"]},"month":"10"},{"date_published":"2021-01-29T00:00:00Z","citation":{"ama":"Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 2021;9(1):1-18. doi:10.1515/agms-2020-0103","ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.","apa":"Ivanov, G., & Tsiutsiurupa, I. (2021). On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. De Gruyter. https://doi.org/10.1515/agms-2020-0103","ieee":"G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” Analysis and Geometry in Metric Spaces, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.","mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces, vol. 9, no. 1, De Gruyter, 2021, pp. 1–18, doi:10.1515/agms-2020-0103.","short":"G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18.","chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces. De Gruyter, 2021. https://doi.org/10.1515/agms-2020-0103."},"publication":"Analysis and Geometry in Metric Spaces","page":"1-18","article_type":"original","has_accepted_license":"1","article_processing_charge":"No","day":"29","scopus_import":"1","keyword":["Applied Mathematics","Geometry and Topology","Analysis"],"oa_version":"Published Version","file":[{"file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":789801,"file_id":"10857","relation":"main_file","date_created":"2022-03-18T09:31:59Z","date_updated":"2022-03-18T09:31:59Z","success":1,"checksum":"7e615ac8489f5eae580b6517debfdc53"}],"_id":"10856","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 9","title":"On the volume of sections of the cube","ddc":["510"],"status":"public","issue":"1","abstract":[{"lang":"eng","text":"We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We \u001cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2."}],"type":"journal_article","doi":"10.1515/agms-2020-0103","language":[{"iso":"eng"}],"external_id":{"isi":["000734286800001"],"arxiv":["2004.02674"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["2299-3274"]},"month":"01","author":[{"last_name":"Ivanov","first_name":"Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"},{"full_name":"Tsiutsiurupa, Igor","last_name":"Tsiutsiurupa","first_name":"Igor"}],"volume":9,"date_updated":"2023-08-17T07:07:58Z","date_created":"2022-03-18T09:25:14Z","year":"2021","acknowledgement":"The authors acknowledge the support of the grant of the Russian Government N 075-15-\r\n2019-1926. G.I.was supported also by the SwissNational Science Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer for valuable remarks.","department":[{"_id":"UlWa"}],"publisher":"De Gruyter","publication_status":"published","file_date_updated":"2022-03-18T09:31:59Z"},{"acknowledgement":"The author was supported by the Swiss National Science Foundation grant 200021_179133. The author acknowledges the financial support from the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no. 075-15-2019-1926.","year":"2021","publication_status":"published","publisher":"Canadian Mathematical Society","department":[{"_id":"UlWa"}],"author":[{"first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"}],"date_created":"2022-03-18T09:55:59Z","date_updated":"2023-09-05T12:43:09Z","volume":64,"oa":1,"external_id":{"isi":["000730165300021"],"arxiv":["1804.10055"]},"main_file_link":[{"url":"https://arxiv.org/abs/1804.10055","open_access":"1"}],"quality_controlled":"1","isi":1,"doi":"10.4153/s000843952000096x","language":[{"iso":"eng"}],"month":"12","publication_identifier":{"issn":["0008-4395"],"eissn":["1496-4287"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10860","title":"Tight frames and related geometric problems","status":"public","intvolume":" 64","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"A tight frame is the orthogonal projection of some orthonormal basis of Rn onto Rk. We show that a set of vectors is a tight frame if and only if the set of all cross products of these vectors is a tight frame. We reformulate a range of problems on the volume of projections (or sections) of regular polytopes in terms of tight frames and write a first-order necessary condition for local extrema of these problems. As applications, we prove new results for the problem of maximization of the volume of zonotopes.","lang":"eng"}],"issue":"4","publication":"Canadian Mathematical Bulletin","citation":{"ama":"Ivanov G. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 2021;64(4):942-963. doi:10.4153/s000843952000096x","ista":"Ivanov G. 2021. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 64(4), 942–963.","apa":"Ivanov, G. (2021). Tight frames and related geometric problems. Canadian Mathematical Bulletin. Canadian Mathematical Society. https://doi.org/10.4153/s000843952000096x","ieee":"G. Ivanov, “Tight frames and related geometric problems,” Canadian Mathematical Bulletin, vol. 64, no. 4. Canadian Mathematical Society, pp. 942–963, 2021.","mla":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin, vol. 64, no. 4, Canadian Mathematical Society, 2021, pp. 942–63, doi:10.4153/s000843952000096x.","short":"G. Ivanov, Canadian Mathematical Bulletin 64 (2021) 942–963.","chicago":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin. Canadian Mathematical Society, 2021. https://doi.org/10.4153/s000843952000096x."},"article_type":"original","page":"942-963","date_published":"2021-12-18T00:00:00Z","scopus_import":"1","keyword":["General Mathematics","Tight frame","Grassmannian","zonotope"],"day":"18","article_processing_charge":"No"},{"language":[{"iso":"eng"}],"doi":"10.1137/1.9781611975994.47","conference":{"location":"Salt Lake City, UT, United States","start_date":"2020-01-05","end_date":"2020-01-08","name":"SODA: Symposium on Discrete Algorithms"},"project":[{"_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312","call_identifier":"FWF","name":"Algorithms for Embeddings and Homotopy Theory"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://doi.org/10.1137/1.9781611975994.47","open_access":"1"}],"publication_identifier":{"isbn":["9781611975994"]},"month":"01","volume":"2020-January","date_updated":"2021-01-12T08:15:38Z","date_created":"2020-05-10T22:00:48Z","author":[{"id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","last_name":"Filakovský","first_name":"Marek","full_name":"Filakovský, Marek"},{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli"},{"last_name":"Zhechev","first_name":"Stephan Y","id":"3AA52972-F248-11E8-B48F-1D18A9856A87","full_name":"Zhechev, Stephan Y"}],"department":[{"_id":"UlWa"}],"publisher":"SIAM","publication_status":"published","year":"2020","date_published":"2020-01-01T00:00:00Z","page":"767-785","citation":{"ieee":"M. Filakovský, U. Wagner, and S. Y. Zhechev, “Embeddability of simplicial complexes is undecidable,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Salt Lake City, UT, United States, 2020, vol. 2020–January, pp. 767–785.","apa":"Filakovský, M., Wagner, U., & Zhechev, S. Y. (2020). Embeddability of simplicial complexes is undecidable. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 2020–January, pp. 767–785). Salt Lake City, UT, United States: SIAM. https://doi.org/10.1137/1.9781611975994.47","ista":"Filakovský M, Wagner U, Zhechev SY. 2020. Embeddability of simplicial complexes is undecidable. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2020–January, 767–785.","ama":"Filakovský M, Wagner U, Zhechev SY. Embeddability of simplicial complexes is undecidable. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 2020-January. SIAM; 2020:767-785. doi:10.1137/1.9781611975994.47","chicago":"Filakovský, Marek, Uli Wagner, and Stephan Y Zhechev. “Embeddability of Simplicial Complexes Is Undecidable.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2020–January:767–85. SIAM, 2020. https://doi.org/10.1137/1.9781611975994.47.","short":"M. Filakovský, U. Wagner, S.Y. Zhechev, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2020, pp. 767–785.","mla":"Filakovský, Marek, et al. “Embeddability of Simplicial Complexes Is Undecidable.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020–January, SIAM, 2020, pp. 767–85, doi:10.1137/1.9781611975994.47."},"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","article_processing_charge":"No","day":"01","scopus_import":1,"oa_version":"Published Version","status":"public","title":"Embeddability of simplicial complexes is undecidable","_id":"7806","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"We consider the following decision problem EMBEDk→d in computational topology (where k ≤ d are fixed positive integers): Given a finite simplicial complex K of dimension k, does there exist a (piecewise-linear) embedding of K into ℝd?\r\nThe special case EMBED1→2 is graph planarity, which is decidable in linear time, as shown by Hopcroft and Tarjan. In higher dimensions, EMBED2→3 and EMBED3→3 are known to be decidable (as well as NP-hard), and recent results of Čadek et al. in computational homotopy theory, in combination with the classical Haefliger–Weber theorem in geometric topology, imply that EMBEDk→d can be solved in polynomial time for any fixed pair (k, d) of dimensions in the so-called metastable range .\r\nHere, by contrast, we prove that EMBEDk→d is algorithmically undecidable for almost all pairs of dimensions outside the metastable range, namely for . This almost completely resolves the decidability vs. undecidability of EMBEDk→d in higher dimensions and establishes a sharp dichotomy between polynomial-time solvability and undecidability.\r\nOur result complements (and in a wide range of dimensions strengthens) earlier results of Matoušek, Tancer, and the second author, who showed that EMBEDk→d is undecidable for 4 ≤ k ϵ {d – 1, d}, and NP-hard for all remaining pairs (k, d) outside the metastable range and satisfying d ≥ 4.","lang":"eng"}],"type":"conference"},{"license":"https://creativecommons.org/licenses/by/3.0/","file_date_updated":"2020-07-14T12:48:06Z","article_number":"12:1 - 12:15","volume":164,"date_created":"2020-06-22T09:14:19Z","date_updated":"2021-01-12T08:16:23Z","author":[{"full_name":"Avvakumov, Sergey","first_name":"Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nivasch, Gabriel","first_name":"Gabriel","last_name":"Nivasch"}],"department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","year":"2020","publication_identifier":{"isbn":["9783959771436"],"issn":["18688969"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2020.12","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2020-06-26","start_date":"2020-06-22","location":"Zürich, Switzerland"},"project":[{"grant_number":"P31312","_id":"26611F5C-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algorithms for Embeddings and Homotopy Theory"}],"quality_controlled":"1","oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1909.00263"]},"abstract":[{"text":"We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between \"grid peeling\" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"8007","checksum":"6872df6549142f709fb6354a1b2f2c06","date_created":"2020-06-23T11:13:49Z","date_updated":"2020-07-14T12:48:06Z","access_level":"open_access","file_name":"2020_LIPIcsSoCG_Avvakumov.pdf","content_type":"application/pdf","file_size":575896,"creator":"dernst"}],"intvolume":" 164","title":"Homotopic curve shortening and the affine curve-shortening flow","status":"public","ddc":["510"],"_id":"7991","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2020-06-01T00:00:00Z","citation":{"ista":"Avvakumov S, Nivasch G. 2020. Homotopic curve shortening and the affine curve-shortening flow. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 12:1-12:15.","ieee":"S. Avvakumov and G. Nivasch, “Homotopic curve shortening and the affine curve-shortening flow,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","apa":"Avvakumov, S., & Nivasch, G. (2020). Homotopic curve shortening and the affine curve-shortening flow. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.12","ama":"Avvakumov S, Nivasch G. Homotopic curve shortening and the affine curve-shortening flow. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.12","chicago":"Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.12.","mla":"Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” 36th International Symposium on Computational Geometry, vol. 164, 12:1-12:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.12.","short":"S. Avvakumov, G. Nivasch, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020."},"publication":"36th International Symposium on Computational Geometry"},{"article_number":"61:1-61:13","file_date_updated":"2020-07-14T12:48:06Z","year":"2020","department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","author":[{"last_name":"Patakova","first_name":"Zuzana","orcid":"0000-0002-3975-1683","id":"48B57058-F248-11E8-B48F-1D18A9856A87","full_name":"Patakova, Zuzana"}],"volume":164,"date_updated":"2021-01-12T08:16:22Z","date_created":"2020-06-22T09:14:18Z","publication_identifier":{"isbn":["9783959771436"],"issn":["18688969"]},"month":"06","external_id":{"arxiv":["1908.01677"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2020.61","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2020-06-26","location":"Zürich, Switzerland","start_date":"2020-06-22"},"language":[{"iso":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"abstract":[{"text":"We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.","lang":"eng"}],"_id":"7989","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 164","status":"public","ddc":["510"],"title":"Bounding radon number via Betti numbers","oa_version":"Published Version","file":[{"date_updated":"2020-07-14T12:48:06Z","date_created":"2020-06-23T06:56:23Z","checksum":"d0996ca5f6eb32ce955ce782b4f2afbe","file_id":"8005","relation":"main_file","creator":"dernst","file_size":645421,"content_type":"application/pdf","file_name":"2020_LIPIcsSoCG_Patakova_61.pdf","access_level":"open_access"}],"scopus_import":"1","has_accepted_license":"1","article_processing_charge":"No","day":"01","citation":{"ieee":"Z. Patakova, “Bounding radon number via Betti numbers,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","apa":"Patakova, Z. (2020). Bounding radon number via Betti numbers. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.61","ista":"Patakova Z. 2020. Bounding radon number via Betti numbers. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 61:1-61:13.","ama":"Patakova Z. Bounding radon number via Betti numbers. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.61","chicago":"Patakova, Zuzana. “Bounding Radon Number via Betti Numbers.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.61.","short":"Z. Patakova, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","mla":"Patakova, Zuzana. “Bounding Radon Number via Betti Numbers.” 36th International Symposium on Computational Geometry, vol. 164, 61:1-61:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.61."},"publication":"36th International Symposium on Computational Geometry","date_published":"2020-06-01T00:00:00Z"},{"article_processing_charge":"No","has_accepted_license":"1","day":"01","scopus_import":1,"date_published":"2020-06-01T00:00:00Z","citation":{"chicago":"Patakova, Zuzana, Martin Tancer, and Uli Wagner. “Barycentric Cuts through a Convex Body.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.62.","mla":"Patakova, Zuzana, et al. “Barycentric Cuts through a Convex Body.” 36th International Symposium on Computational Geometry, vol. 164, 62:1-62:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.62.","short":"Z. Patakova, M. Tancer, U. Wagner, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ista":"Patakova Z, Tancer M, Wagner U. 2020. Barycentric cuts through a convex body. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 62:1-62:16.","ieee":"Z. Patakova, M. Tancer, and U. Wagner, “Barycentric cuts through a convex body,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","apa":"Patakova, Z., Tancer, M., & Wagner, U. (2020). Barycentric cuts through a convex body. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.62","ama":"Patakova Z, Tancer M, Wagner U. Barycentric cuts through a convex body. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.62"},"publication":"36th International Symposium on Computational Geometry","abstract":[{"lang":"eng","text":"Let K be a convex body in ℝⁿ (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K ∩ h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p₀ is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n ≥ 2, there are always at least three distinct barycentric cuts through the point p₀ ∈ K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p₀ are guaranteed if n ≥ 3."}],"alternative_title":["LIPIcs"],"type":"conference","file":[{"relation":"main_file","file_id":"8004","date_updated":"2020-07-14T12:48:06Z","date_created":"2020-06-23T06:45:52Z","checksum":"ce1c9194139a664fb59d1efdfc88eaae","file_name":"2020_LIPIcsSoCG_Patakova.pdf","access_level":"open_access","content_type":"application/pdf","file_size":750318,"creator":"dernst"}],"oa_version":"Published Version","intvolume":" 164","status":"public","ddc":["510"],"title":"Barycentric cuts through a convex body","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7992","publication_identifier":{"issn":["18688969"],"isbn":["9783959771436"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2020.62","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2020-06-22","location":"Zürich, Switzerland","end_date":"2020-06-26"},"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2003.13536"]},"oa":1,"file_date_updated":"2020-07-14T12:48:06Z","article_number":"62:1 - 62:16","volume":164,"date_updated":"2021-01-12T08:16:23Z","date_created":"2020-06-22T09:14:20Z","author":[{"full_name":"Patakova, Zuzana","id":"48B57058-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3975-1683","first_name":"Zuzana","last_name":"Patakova"},{"first_name":"Martin","last_name":"Tancer","id":"38AC689C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1191-6714","full_name":"Tancer, Martin"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","year":"2020"},{"abstract":[{"text":"In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of K_n was found recently. We extend this characterization to all graphs, by describing the set of minimal forbidden subdrawings for pseudolinear drawings. Our characterization also leads to a polynomial-time algorithm to recognize pseudolinear drawings and construct the pseudolines when it is possible.","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"file":[{"checksum":"93571b76cf97d5b7c8aabaeaa694dd7e","date_updated":"2020-07-14T12:48:06Z","date_created":"2020-06-23T11:06:23Z","relation":"main_file","file_id":"8006","file_size":592661,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2020_LIPIcsSoCG_Arroyo.pdf"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7994","title":"Extending drawings of graphs to arrangements of pseudolines","ddc":["510"],"status":"public","intvolume":" 164","day":"01","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2020-06-01T00:00:00Z","publication":"36th International Symposium on Computational Geometry","citation":{"ista":"Arroyo Guevara AM, Bensmail J, Bruce Richter R. 2020. Extending drawings of graphs to arrangements of pseudolines. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 9:1-9:14.","ieee":"A. M. Arroyo Guevara, J. Bensmail, and R. Bruce Richter, “Extending drawings of graphs to arrangements of pseudolines,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","apa":"Arroyo Guevara, A. M., Bensmail, J., & Bruce Richter, R. (2020). Extending drawings of graphs to arrangements of pseudolines. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.9","ama":"Arroyo Guevara AM, Bensmail J, Bruce Richter R. Extending drawings of graphs to arrangements of pseudolines. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.9","chicago":"Arroyo Guevara, Alan M, Julien Bensmail, and R. Bruce Richter. “Extending Drawings of Graphs to Arrangements of Pseudolines.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.9.","mla":"Arroyo Guevara, Alan M., et al. “Extending Drawings of Graphs to Arrangements of Pseudolines.” 36th International Symposium on Computational Geometry, vol. 164, 9:1-9:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.9.","short":"A.M. Arroyo Guevara, J. Bensmail, R. Bruce Richter, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020."},"file_date_updated":"2020-07-14T12:48:06Z","ec_funded":1,"article_number":"9:1 - 9:14","author":[{"id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","first_name":"Alan M","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M"},{"full_name":"Bensmail, Julien","last_name":"Bensmail","first_name":"Julien"},{"full_name":"Bruce Richter, R.","first_name":"R.","last_name":"Bruce Richter"}],"date_created":"2020-06-22T09:14:21Z","date_updated":"2023-02-23T13:22:12Z","volume":164,"year":"2020","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","month":"06","publication_identifier":{"issn":["18688969"],"isbn":["9783959771436"]},"conference":{"end_date":"2020-06-26","location":"Zürich, Switzerland","start_date":"2020-06-22","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2020.9","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1804.09317"]},"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}]},{"month":"06","publication_identifier":{"isbn":["9783959771436"],"issn":["18688969"]},"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2003.13557"]},"language":[{"iso":"eng"}],"conference":{"end_date":"2020-06-26","location":"Zürich, Switzerland","start_date":"2020-06-22","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2020.67","article_number":"67:1 - 67:16","file_date_updated":"2020-07-14T12:48:06Z","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"year":"2020","date_created":"2020-06-22T09:14:19Z","date_updated":"2023-08-04T08:51:07Z","volume":164,"author":[{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"12129"}]},"scopus_import":1,"day":"01","has_accepted_license":"1","article_processing_charge":"No","publication":"36th International Symposium on Computational Geometry","citation":{"chicago":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part II: Bistellar Flips).” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.67.","mla":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part II: Bistellar Flips).” 36th International Symposium on Computational Geometry, vol. 164, 67:1-67:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.67.","short":"U. Wagner, E. Welzl, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ista":"Wagner U, Welzl E. 2020. Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips). 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 67:1-67:16.","apa":"Wagner, U., & Welzl, E. (2020). Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips). In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.67","ieee":"U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips),” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","ama":"Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips). In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.67"},"date_published":"2020-06-01T00:00:00Z","alternative_title":["LIPIcs"],"type":"conference","abstract":[{"lang":"eng","text":"Given a finite point set P in general position in the plane, a full triangulation is a maximal straight-line embedded plane graph on P. A partial triangulation on P is a full triangulation of some subset P' of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge, removes a non-extreme point of degree 3, or adds a point in P ⧵ P' as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The goal of this paper is to investigate the structure of this graph, with emphasis on its connectivity. For sets P of n points in general position, we show that the bistellar flip graph is (n-3)-connected, thereby answering, for sets in general position, an open questions raised in a book (by De Loera, Rambau, and Santos) and a survey (by Lee and Santos) on triangulations. This matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points and projecting the lower convex hull), where (n-3)-connectivity has been known since the late 1980s through the secondary polytope (Gelfand, Kapranov, Zelevinsky) and Balinski’s Theorem. Our methods also yield the following results (see the full version [Wagner and Welzl, 2020]): (i) The bistellar flip graph can be covered by graphs of polytopes of dimension n-3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n-3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations are regular iff the trivial subdivision has height n-3 in the partial order of partial subdivisions. (iv) There are arbitrarily large sets P with non-regular partial triangulations, while every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular partial triangulations (answering a question by F. Santos in the unexpected direction)."}],"ddc":["510"],"title":"Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips)","status":"public","intvolume":" 164","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7990","file":[{"creator":"dernst","content_type":"application/pdf","file_size":793187,"access_level":"open_access","file_name":"2020_LIPIcsSoCG_Wagner.pdf","checksum":"3f6925be5f3dcdb3b14cab92f410edf7","date_updated":"2020-07-14T12:48:06Z","date_created":"2020-06-23T06:37:27Z","file_id":"8003","relation":"main_file"}],"oa_version":"Published Version"},{"language":[{"iso":"eng"}],"doi":"10.1137/1.9781611975994.172","conference":{"name":"SODA: Symposium on Discrete Algorithms","start_date":"2020-01-05","location":"Salt Lake City, UT, United States","end_date":"2020-01-08"},"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.1137/1.9781611975994.172","open_access":"1"}],"external_id":{"arxiv":["2003.13557"]},"oa":1,"publication_identifier":{"isbn":["9781611975994"]},"month":"01","volume":"2020-January","date_created":"2020-05-10T22:00:48Z","date_updated":"2023-08-04T08:51:07Z","related_material":{"record":[{"status":"public","relation":"later_version","id":"12129"}]},"author":[{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"department":[{"_id":"UlWa"}],"publisher":"SIAM","publication_status":"published","year":"2020","date_published":"2020-01-01T00:00:00Z","page":"2823-2841","citation":{"mla":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part I: Edge Flips).” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020–January, SIAM, 2020, pp. 2823–41, doi:10.1137/1.9781611975994.172.","short":"U. Wagner, E. Welzl, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2020, pp. 2823–2841.","chicago":"Wagner, Uli, and Emo Welzl. “Connectivity of Triangulation Flip Graphs in the Plane (Part I: Edge Flips).” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2020–January:2823–41. SIAM, 2020. https://doi.org/10.1137/1.9781611975994.172.","ama":"Wagner U, Welzl E. Connectivity of triangulation flip graphs in the plane (Part I: Edge flips). In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 2020-January. SIAM; 2020:2823-2841. doi:10.1137/1.9781611975994.172","ista":"Wagner U, Welzl E. 2020. Connectivity of triangulation flip graphs in the plane (Part I: Edge flips). Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2020–January, 2823–2841.","ieee":"U. Wagner and E. Welzl, “Connectivity of triangulation flip graphs in the plane (Part I: Edge flips),” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Salt Lake City, UT, United States, 2020, vol. 2020–January, pp. 2823–2841.","apa":"Wagner, U., & Welzl, E. (2020). Connectivity of triangulation flip graphs in the plane (Part I: Edge flips). In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 2020–January, pp. 2823–2841). Salt Lake City, UT, United States: SIAM. https://doi.org/10.1137/1.9781611975994.172"},"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","article_processing_charge":"No","day":"01","scopus_import":1,"oa_version":"Submitted Version","title":"Connectivity of triangulation flip graphs in the plane (Part I: Edge flips)","status":"public","_id":"7807","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"In a straight-line embedded triangulation of a point set P in the plane, removing an inner edge and—provided the resulting quadrilateral is convex—adding the other diagonal is called an edge flip. The (edge) flip graph has all triangulations as vertices, and a pair of triangulations is adjacent if they can be obtained from each other by an edge flip. The goal of this paper is to contribute to a better understanding of the flip graph, with an emphasis on its connectivity.\r\nFor sets in general position, it is known that every triangulation allows at least edge flips (a tight bound) which gives the minimum degree of any flip graph for n points. We show that for every point set P in general position, the flip graph is at least -vertex connected. Somewhat more strongly, we show that the vertex connectivity equals the minimum degree occurring in the flip graph, i.e. the minimum number of flippable edges in any triangulation of P, provided P is large enough. Finally, we exhibit some of the geometry of the flip graph by showing that the flip graph can be covered by 1-skeletons of polytopes of dimension (products of associahedra).\r\nA corresponding result ((n – 3)-vertex connectedness) can be shown for the bistellar flip graph of partial triangulations, i.e. the set of all triangulations of subsets of P which contain all extreme points of P. This will be treated separately in a second part."}],"type":"conference"},{"scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Russian Mathematical Surveys","citation":{"ieee":"S. Avvakumov, U. Wagner, I. Mabillard, and A. B. Skopenkov, “Eliminating higher-multiplicity intersections, III. Codimension 2,” Russian Mathematical Surveys, vol. 75, no. 6. IOP Publishing, pp. 1156–1158, 2020.","apa":"Avvakumov, S., Wagner, U., Mabillard, I., & Skopenkov, A. B. (2020). Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM9943","ista":"Avvakumov S, Wagner U, Mabillard I, Skopenkov AB. 2020. Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. 75(6), 1156–1158.","ama":"Avvakumov S, Wagner U, Mabillard I, Skopenkov AB. Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. 2020;75(6):1156-1158. doi:10.1070/RM9943","chicago":"Avvakumov, Sergey, Uli Wagner, Isaac Mabillard, and A. B. Skopenkov. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” Russian Mathematical Surveys. IOP Publishing, 2020. https://doi.org/10.1070/RM9943.","short":"S. Avvakumov, U. Wagner, I. Mabillard, A.B. Skopenkov, Russian Mathematical Surveys 75 (2020) 1156–1158.","mla":"Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections, III. Codimension 2.” Russian Mathematical Surveys, vol. 75, no. 6, IOP Publishing, 2020, pp. 1156–58, doi:10.1070/RM9943."},"article_type":"original","page":"1156-1158","date_published":"2020-12-01T00:00:00Z","type":"journal_article","issue":"6","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9308","title":"Eliminating higher-multiplicity intersections, III. Codimension 2","status":"public","intvolume":" 75","oa_version":"Preprint","month":"12","publication_identifier":{"issn":["0036-0279"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1511.03501"}],"oa":1,"external_id":{"isi":["000625983100001"],"arxiv":["1511.03501"]},"isi":1,"quality_controlled":"1","doi":"10.1070/RM9943","language":[{"iso":"eng"}],"year":"2020","acknowledgement":"This research was carried out with the support of the Russian Foundation for Basic Research(grant no. 19-01-00169)","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"IOP Publishing","author":[{"last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli"},{"id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","first_name":"Isaac","last_name":"Mabillard","full_name":"Mabillard, Isaac"},{"full_name":"Skopenkov, A. B.","last_name":"Skopenkov","first_name":"A. B."}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"8183"},{"id":"10220","relation":"later_version","status":"public"}]},"date_updated":"2023-08-14T11:43:54Z","date_created":"2021-04-04T22:01:22Z","volume":75},{"date_published":"2020-04-01T00:00:00Z","publication":"Foundations of Computational Mathematics","citation":{"chicago":"Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An Algorithmic Viewpoint.” Foundations of Computational Mathematics. Springer Nature, 2020. https://doi.org/10.1007/s10208-019-09419-x.","short":"M. Filakovský, L. Vokřínek, Foundations of Computational Mathematics 20 (2020) 311–330.","mla":"Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An Algorithmic Viewpoint.” Foundations of Computational Mathematics, vol. 20, Springer Nature, 2020, pp. 311–30, doi:10.1007/s10208-019-09419-x.","ieee":"M. Filakovský and L. Vokřínek, “Are two given maps homotopic? An algorithmic viewpoint,” Foundations of Computational Mathematics, vol. 20. Springer Nature, pp. 311–330, 2020.","apa":"Filakovský, M., & Vokřínek, L. (2020). Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-019-09419-x","ista":"Filakovský M, Vokřínek L. 2020. Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. 20, 311–330.","ama":"Filakovský M, Vokřínek L. Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. 2020;20:311-330. doi:10.1007/s10208-019-09419-x"},"article_type":"original","page":"311-330","day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6563","status":"public","title":"Are two given maps homotopic? An algorithmic viewpoint","intvolume":" 20","abstract":[{"text":"This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.","lang":"eng"}],"type":"journal_article","doi":"10.1007/s10208-019-09419-x","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1312.2337"}],"external_id":{"arxiv":["1312.2337"],"isi":["000522437400004"]},"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FWF","name":"Algorithms for Embeddings and Homotopy Theory","_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312"}],"month":"04","publication_identifier":{"issn":["16153375"],"eissn":["16153383"]},"author":[{"full_name":"Filakovský, Marek","first_name":"Marek","last_name":"Filakovský","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vokřínek, Lukas","first_name":"Lukas","last_name":"Vokřínek"}],"date_updated":"2023-08-17T13:50:44Z","date_created":"2019-06-16T21:59:14Z","volume":20,"year":"2020","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"UlWa"}]},{"oa_version":"Preprint","_id":"7960","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Intersection patterns of planar sets","status":"public","intvolume":" 64","abstract":[{"lang":"eng","text":"Let A={A1,…,An} be a family of sets in the plane. For 0≤i2b be integers. We prove that if each k-wise or (k+1)-wise intersection of sets from A has at most b path-connected components, which all are open, then fk+1=0 implies fk≤cfk−1 for some positive constant c depending only on b and k. These results also extend to two-dimensional compact surfaces."}],"type":"journal_article","date_published":"2020-09-01T00:00:00Z","publication":"Discrete and Computational Geometry","citation":{"chicago":"Kalai, Gil, and Zuzana Patakova. “Intersection Patterns of Planar Sets.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00205-z.","short":"G. Kalai, Z. Patakova, Discrete and Computational Geometry 64 (2020) 304–323.","mla":"Kalai, Gil, and Zuzana Patakova. “Intersection Patterns of Planar Sets.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 304–23, doi:10.1007/s00454-020-00205-z.","ieee":"G. Kalai and Z. Patakova, “Intersection patterns of planar sets,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 304–323, 2020.","apa":"Kalai, G., & Patakova, Z. (2020). Intersection patterns of planar sets. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00205-z","ista":"Kalai G, Patakova Z. 2020. Intersection patterns of planar sets. Discrete and Computational Geometry. 64, 304–323.","ama":"Kalai G, Patakova Z. Intersection patterns of planar sets. Discrete and Computational Geometry. 2020;64:304-323. doi:10.1007/s00454-020-00205-z"},"article_type":"original","page":"304-323","day":"01","article_processing_charge":"No","scopus_import":"1","author":[{"full_name":"Kalai, Gil","first_name":"Gil","last_name":"Kalai"},{"orcid":"0000-0002-3975-1683","id":"48B57058-F248-11E8-B48F-1D18A9856A87","last_name":"Patakova","first_name":"Zuzana","full_name":"Patakova, Zuzana"}],"date_updated":"2023-08-21T08:26:34Z","date_created":"2020-06-14T22:00:50Z","volume":64,"year":"2020","acknowledgement":"We are very grateful to Pavel Paták for many helpful discussions and remarks. We also thank the referees for helpful comments, which greatly improved the presentation.\r\nThe project was supported by ERC Advanced Grant 320924. GK was also partially supported by NSF grant DMS1300120. The research stay of ZP at IST Austria is funded by the project CZ.02.2.69/0.0/0.0/17_050/0008466 Improvement of internationalization in the field of research and development at Charles University, through the support of quality projects MSCA-IF.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"doi":"10.1007/s00454-020-00205-z","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1907.00885","open_access":"1"}],"external_id":{"isi":["000537329400001"],"arxiv":["1907.00885"]},"isi":1,"quality_controlled":"1","month":"09","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]}},{"day":"09","article_processing_charge":"No","scopus_import":"1","date_published":"2020-10-09T00:00:00Z","publication":"Graph-Theoretic Concepts in Computer Science","citation":{"short":"A.M. Arroyo Guevara, F. Klute, I. Parada, R. Seidel, B. Vogtenhuber, T. Wiedera, in:, Graph-Theoretic Concepts in Computer Science, Springer Nature, 2020, pp. 325–338.","mla":"Arroyo Guevara, Alan M., et al. “Inserting One Edge into a Simple Drawing Is Hard.” Graph-Theoretic Concepts in Computer Science, vol. 12301, Springer Nature, 2020, pp. 325–38, doi:10.1007/978-3-030-60440-0_26.","chicago":"Arroyo Guevara, Alan M, Fabian Klute, Irene Parada, Raimund Seidel, Birgit Vogtenhuber, and Tilo Wiedera. “Inserting One Edge into a Simple Drawing Is Hard.” In Graph-Theoretic Concepts in Computer Science, 12301:325–38. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-60440-0_26.","ama":"Arroyo Guevara AM, Klute F, Parada I, Seidel R, Vogtenhuber B, Wiedera T. Inserting one edge into a simple drawing is hard. In: Graph-Theoretic Concepts in Computer Science. Vol 12301. Springer Nature; 2020:325-338. doi:10.1007/978-3-030-60440-0_26","ieee":"A. M. Arroyo Guevara, F. Klute, I. Parada, R. Seidel, B. Vogtenhuber, and T. Wiedera, “Inserting one edge into a simple drawing is hard,” in Graph-Theoretic Concepts in Computer Science, Leeds, United Kingdom, 2020, vol. 12301, pp. 325–338.","apa":"Arroyo Guevara, A. M., Klute, F., Parada, I., Seidel, R., Vogtenhuber, B., & Wiedera, T. (2020). Inserting one edge into a simple drawing is hard. In Graph-Theoretic Concepts in Computer Science (Vol. 12301, pp. 325–338). Leeds, United Kingdom: Springer Nature. https://doi.org/10.1007/978-3-030-60440-0_26","ista":"Arroyo Guevara AM, Klute F, Parada I, Seidel R, Vogtenhuber B, Wiedera T. 2020. Inserting one edge into a simple drawing is hard. Graph-Theoretic Concepts in Computer Science. WG: Workshop on Graph-Theoretic Concepts in Computer Science, LNCS, vol. 12301, 325–338."},"page":"325-338","abstract":[{"text":"A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP -complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ , it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"None","_id":"8732","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Inserting one edge into a simple drawing is hard","status":"public","intvolume":" 12301","month":"10","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030604394","9783030604400"],"issn":["0302-9743"]},"conference":{"end_date":"2020-06-26","location":"Leeds, United Kingdom","start_date":"2020-06-24","name":"WG: Workshop on Graph-Theoretic Concepts in Computer Science"},"doi":"10.1007/978-3-030-60440-0_26","language":[{"iso":"eng"}],"quality_controlled":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"ec_funded":1,"author":[{"orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","first_name":"Alan M","full_name":"Arroyo Guevara, Alan M"},{"full_name":"Klute, Fabian","last_name":"Klute","first_name":"Fabian"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"},{"last_name":"Vogtenhuber","first_name":"Birgit","full_name":"Vogtenhuber, Birgit"},{"first_name":"Tilo","last_name":"Wiedera","full_name":"Wiedera, Tilo"}],"date_created":"2020-11-06T08:45:03Z","date_updated":"2023-09-05T15:09:16Z","volume":12301,"year":"2020","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer Nature"},{"keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"day":"09","has_accepted_license":"1","article_processing_charge":"No","citation":{"ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","apa":"Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944."},"page":"160","date_published":"2020-06-09T00:00:00Z","type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.","lang":"eng"}],"_id":"7944","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Reconfiguration problems","ddc":["516","514"],"file":[{"access_level":"open_access","file_name":"THESIS_Zuzka_Masarova.pdf","creator":"zmasarov","content_type":"application/pdf","file_size":13661779,"file_id":"7945","relation":"main_file","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:34:00Z"},{"content_type":"application/zip","file_size":32184006,"creator":"zmasarov","access_level":"closed","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","checksum":"45341a35b8f5529c74010b7af43ac188","date_created":"2020-06-08T00:35:30Z","date_updated":"2020-07-14T12:48:05Z","relation":"source_file","file_id":"7946"}],"oa_version":"Published Version","month":"06","publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"oa":1,"tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"doi":"10.15479/AT:ISTA:7944","supervisor":[{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"degree_awarded":"PhD","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:48:05Z","license":"https://creativecommons.org/licenses/by-sa/4.0/","year":"2020","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publisher":"Institute of Science and Technology Austria","author":[{"orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana","full_name":"Masárová, Zuzana"}],"related_material":{"record":[{"id":"7950","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"5986"}]},"date_created":"2020-06-08T00:49:46Z","date_updated":"2023-09-07T13:17:37Z"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"doi":"10.15479/AT:ISTA:8032","acknowledged_ssus":[{"_id":"E-Lib"},{"_id":"CampIT"}],"degree_awarded":"PhD","supervisor":[{"first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli"},{"first_name":"Jonathan","last_name":"Spreer","full_name":"Spreer, Jonathan"}],"language":[{"iso":"eng"}],"month":"06","publication_identifier":{"isbn":["978-3-99078-006-0"],"issn":["2663-337X"]},"year":"2020","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Institute of Science and Technology Austria","author":[{"orcid":"0000-0002-5445-5057","id":"33C26278-F248-11E8-B48F-1D18A9856A87","last_name":"Huszár","first_name":"Kristóf","full_name":"Huszár, Kristóf"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6556"},{"id":"7093","relation":"dissertation_contains","status":"public"}]},"date_updated":"2023-09-07T13:18:27Z","date_created":"2020-06-26T10:00:36Z","file_date_updated":"2020-07-14T12:48:08Z","citation":{"mla":"Huszár, Kristóf. Combinatorial Width Parameters for 3-Dimensional Manifolds. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:8032.","short":"K. Huszár, Combinatorial Width Parameters for 3-Dimensional Manifolds, Institute of Science and Technology Austria, 2020.","chicago":"Huszár, Kristóf. “Combinatorial Width Parameters for 3-Dimensional Manifolds.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:8032.","ama":"Huszár K. Combinatorial width parameters for 3-dimensional manifolds. 2020. doi:10.15479/AT:ISTA:8032","ista":"Huszár K. 2020. Combinatorial width parameters for 3-dimensional manifolds. Institute of Science and Technology Austria.","ieee":"K. Huszár, “Combinatorial width parameters for 3-dimensional manifolds,” Institute of Science and Technology Austria, 2020.","apa":"Huszár, K. (2020). Combinatorial width parameters for 3-dimensional manifolds. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:8032"},"page":"xviii+120","date_published":"2020-06-26T00:00:00Z","day":"26","has_accepted_license":"1","article_processing_charge":"No","_id":"8032","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Combinatorial width parameters for 3-dimensional manifolds","ddc":["514"],"file":[{"checksum":"bd8be6e4f1addc863dfcc0fad29ee9c3","date_created":"2020-06-26T10:03:58Z","date_updated":"2020-07-14T12:48:08Z","file_id":"8034","relation":"main_file","creator":"khuszar","file_size":2637562,"content_type":"application/pdf","access_level":"open_access","file_name":"Kristof_Huszar-Thesis.pdf"},{"checksum":"d5f8456202b32f4a77552ef47a2837d1","date_created":"2020-06-26T10:10:06Z","date_updated":"2020-07-14T12:48:08Z","file_id":"8035","relation":"source_file","creator":"khuszar","content_type":"application/x-zip-compressed","file_size":7163491,"access_level":"closed","file_name":"Kristof_Huszar-Thesis-source.zip"}],"oa_version":"Published Version","type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"lang":"eng","text":"Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.”\r\nIn this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus."}]},{"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"8182"},{"status":"public","relation":"part_of_dissertation","id":"8183"},{"status":"public","relation":"part_of_dissertation","id":"8185"},{"relation":"part_of_dissertation","status":"public","id":"8184"},{"id":"6355","status":"public","relation":"part_of_dissertation"},{"id":"75","status":"public","relation":"part_of_dissertation"}]},"author":[{"full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","first_name":"Sergey"}],"date_created":"2020-07-23T09:51:29Z","date_updated":"2023-12-18T10:51:01Z","year":"2020","publisher":"Institute of Science and Technology Austria","department":[{"_id":"UlWa"}],"publication_status":"published","file_date_updated":"2020-07-27T12:46:53Z","doi":"10.15479/AT:ISTA:8156","language":[{"iso":"eng"}],"supervisor":[{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli"}],"degree_awarded":"PhD","oa":1,"publication_identifier":{"issn":["2663-337X"]},"month":"07","file":[{"relation":"source_file","file_id":"8178","date_created":"2020-07-27T12:44:51Z","date_updated":"2020-07-27T12:44:51Z","file_name":"source.zip","access_level":"closed","content_type":"application/zip","file_size":1061740,"creator":"savvakum"},{"success":1,"date_updated":"2020-07-27T12:46:53Z","date_created":"2020-07-27T12:46:53Z","relation":"main_file","file_id":"8179","content_type":"application/pdf","file_size":1336501,"creator":"savvakum","access_level":"open_access","file_name":"thesis_pdfa.pdf"}],"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"8156","status":"public","ddc":["514"],"title":"Topological methods in geometry and discrete mathematics","abstract":[{"lang":"eng","text":"We present solutions to several problems originating from geometry and discrete mathematics: existence of equipartitions, maps without Tverberg multiple points, and inscribing quadrilaterals. Equivariant obstruction theory is the natural topological approach to these type of questions. However, for the specific problems we consider it had yielded only partial or no results. We get our results by complementing equivariant obstruction theory with other techniques from topology and geometry."}],"type":"dissertation","alternative_title":["ISTA Thesis"],"date_published":"2020-07-24T00:00:00Z","citation":{"ama":"Avvakumov S. Topological methods in geometry and discrete mathematics. 2020. doi:10.15479/AT:ISTA:8156","ista":"Avvakumov S. 2020. Topological methods in geometry and discrete mathematics. Institute of Science and Technology Austria.","apa":"Avvakumov, S. (2020). Topological methods in geometry and discrete mathematics. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:8156","ieee":"S. Avvakumov, “Topological methods in geometry and discrete mathematics,” Institute of Science and Technology Austria, 2020.","mla":"Avvakumov, Sergey. Topological Methods in Geometry and Discrete Mathematics. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:8156.","short":"S. Avvakumov, Topological Methods in Geometry and Discrete Mathematics, Institute of Science and Technology Austria, 2020.","chicago":"Avvakumov, Sergey. “Topological Methods in Geometry and Discrete Mathematics.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:8156."},"page":"119","article_processing_charge":"No","has_accepted_license":"1","day":"24"},{"language":[{"iso":"eng"}],"date_published":"2020-04-01T00:00:00Z","conference":{"name":"EuroCG: European Workshop on Computational Geometry","location":"Würzburg, Germany, Virtual","start_date":"2020-03-16","end_date":"2020-03-18"},"quality_controlled":"1","citation":{"chicago":"Aichholzer, Oswin, Julia Obmann, Pavel Patak, Daniel Perz, and Josef Tkadlec. “Disjoint Tree-Compatible Plane Perfect Matchings.” In 36th European Workshop on Computational Geometry, 2020.","short":"O. Aichholzer, J. Obmann, P. Patak, D. Perz, J. Tkadlec, in:, 36th European Workshop on Computational Geometry, 2020.","mla":"Aichholzer, Oswin, et al. “Disjoint Tree-Compatible Plane Perfect Matchings.” 36th European Workshop on Computational Geometry, 56, 2020.","apa":"Aichholzer, O., Obmann, J., Patak, P., Perz, D., & Tkadlec, J. (2020). Disjoint tree-compatible plane perfect matchings. In 36th European Workshop on Computational Geometry. Würzburg, Germany, Virtual.","ieee":"O. Aichholzer, J. Obmann, P. Patak, D. Perz, and J. Tkadlec, “Disjoint tree-compatible plane perfect matchings,” in 36th European Workshop on Computational Geometry, Würzburg, Germany, Virtual, 2020.","ista":"Aichholzer O, Obmann J, Patak P, Perz D, Tkadlec J. 2020. Disjoint tree-compatible plane perfect matchings. 36th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 56.","ama":"Aichholzer O, Obmann J, Patak P, Perz D, Tkadlec J. Disjoint tree-compatible plane perfect matchings. In: 36th European Workshop on Computational Geometry. ; 2020."},"oa":1,"main_file_link":[{"url":"https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/data/uploads/papers/eurocg20_paper_56.pdf","open_access":"1"}],"publication":"36th European Workshop on Computational Geometry","article_processing_charge":"No","month":"04","day":"01","oa_version":"Published Version","date_created":"2024-03-05T08:57:17Z","date_updated":"2024-03-05T09:00:07Z","author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"last_name":"Obmann","first_name":"Julia","full_name":"Obmann, Julia"},{"full_name":"Patak, Pavel","last_name":"Patak","first_name":"Pavel","id":"B593B804-1035-11EA-B4F1-947645A5BB83"},{"full_name":"Perz, Daniel","first_name":"Daniel","last_name":"Perz"},{"last_name":"Tkadlec","first_name":"Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef"}],"department":[{"_id":"KrCh"},{"_id":"UlWa"}],"title":"Disjoint tree-compatible plane perfect matchings","publication_status":"published","status":"public","acknowledgement":"Research on this work was initiated at the 6th Austrian-Japanese-Mexican-Spanish Workshop on Discrete Geometry and continued during the 16th European Geometric Graph-Week, both held near Strobl, Austria. We are grateful to the participants for the inspiring atmosphere. We especially thank Alexander Pilz for bringing this class of problems to our attention and Birgit Vogtenhuber for inspiring discussions. D.P. is partially supported by the FWF grant I 3340-N35 (Collaborative DACH project Arrangements and Drawings). The research stay of P.P. at IST Austria is funded by the project CZ.02.2.69/0.0/0.0/17_050/0008466 Improvement of internationalization in the field of research and development at Charles University, through the support of quality projects MSCA-IF. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922.","_id":"15082","year":"2020","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Two plane drawings of geometric graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. For a given set S of 2n points two plane drawings of perfect matchings M1 and M2 (which do not need to be disjoint nor compatible) are disjoint tree-compatible if there exists a plane drawing of a spanning tree T on S which is disjoint compatible to both M1 and M2.\r\nWe show that the graph of all disjoint tree-compatible perfect geometric matchings on 2n points in convex position is connected if and only if 2n ≥ 10. Moreover, in that case the diameter\r\nof this graph is either 4 or 5, independent of n.","lang":"eng"}],"type":"conference","article_number":"56"},{"month":"06","publication_identifier":{"isbn":["978-3-95977-104-7"],"issn":["1868-8969"]},"language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Portland, OR, United States","start_date":"2019-06-18","end_date":"2019-06-21"},"doi":"10.4230/LIPICS.SOCG.2019.39","quality_controlled":"1","project":[{"name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF","_id":"261FA626-B435-11E9-9278-68D0E5697425","grant_number":"M02281"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1903.08637"]},"oa":1,"file_date_updated":"2020-07-14T12:47:57Z","article_number":"39","date_updated":"2021-01-12T08:13:24Z","date_created":"2020-01-29T16:17:05Z","volume":129,"author":[{"full_name":"Fulek, Radoslav","first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774"},{"full_name":"Kyncl, Jan","first_name":"Jan","last_name":"Kyncl"}],"publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2019","day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":1,"date_published":"2019-06-01T00:00:00Z","publication":"35th International Symposium on Computational Geometry (SoCG 2019)","citation":{"ama":"Fulek R, Kyncl J. Z_2-Genus of graphs and minimum rank of partial symmetric matrices. In: 35th International Symposium on Computational Geometry (SoCG 2019). Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019. doi:10.4230/LIPICS.SOCG.2019.39","ieee":"R. Fulek and J. Kyncl, “Z_2-Genus of graphs and minimum rank of partial symmetric matrices,” in 35th International Symposium on Computational Geometry (SoCG 2019), Portland, OR, United States, 2019, vol. 129.","apa":"Fulek, R., & Kyncl, J. (2019). Z_2-Genus of graphs and minimum rank of partial symmetric matrices. In 35th International Symposium on Computational Geometry (SoCG 2019) (Vol. 129). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.39","ista":"Fulek R, Kyncl J. 2019. Z_2-Genus of graphs and minimum rank of partial symmetric matrices. 35th International Symposium on Computational Geometry (SoCG 2019). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 129, 39.","short":"R. Fulek, J. Kyncl, in:, 35th International Symposium on Computational Geometry (SoCG 2019), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019.","mla":"Fulek, Radoslav, and Jan Kyncl. “Z_2-Genus of Graphs and Minimum Rank of Partial Symmetric Matrices.” 35th International Symposium on Computational Geometry (SoCG 2019), vol. 129, 39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, doi:10.4230/LIPICS.SOCG.2019.39.","chicago":"Fulek, Radoslav, and Jan Kyncl. “Z_2-Genus of Graphs and Minimum Rank of Partial Symmetric Matrices.” In 35th International Symposium on Computational Geometry (SoCG 2019), Vol. 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.39."},"abstract":[{"lang":"eng","text":"The genus g(G) of a graph G is the minimum g such that G has an embedding on the orientable surface M_g of genus g. A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The Z_2-genus of a graph G, denoted by g_0(G), is the minimum g such that G has an independently even drawing on M_g. By a result of Battle, Harary, Kodama and Youngs from 1962, the graph genus is additive over 2-connected blocks. In 2013, Schaefer and Stefankovic proved that the Z_2-genus of a graph is additive over 2-connected blocks as well, and asked whether this result can be extended to so-called 2-amalgamations, as an analogue of results by Decker, Glover, Huneke, and Stahl for the genus. We give the following partial answer. If G=G_1 cup G_2, G_1 and G_2 intersect in two vertices u and v, and G-u-v has k connected components (among which we count the edge uv if present), then |g_0(G)-(g_0(G_1)+g_0(G_2))|<=k+1. For complete bipartite graphs K_{m,n}, with n >= m >= 3, we prove that g_0(K_{m,n})/g(K_{m,n})=1-O(1/n). Similar results are proved also for the Euler Z_2-genus. We express the Z_2-genus of a graph using the minimum rank of partial symmetric matrices over Z_2; a problem that might be of independent interest. "}],"alternative_title":["LIPIcs"],"type":"conference","oa_version":"Published Version","file":[{"checksum":"aac37b09118cc0ab58cf77129e691f8c","date_updated":"2020-07-14T12:47:57Z","date_created":"2020-02-04T09:14:31Z","file_id":"7445","relation":"main_file","creator":"dernst","file_size":628347,"content_type":"application/pdf","access_level":"open_access","file_name":"2019_LIPIcs_Fulek.pdf"}],"status":"public","title":"Z_2-Genus of graphs and minimum rank of partial symmetric matrices","ddc":["000"],"intvolume":" 129","_id":"7401","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"publication_identifier":{"issn":["03649024"]},"month":"08","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"isi":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1309.2399","open_access":"1"}],"oa":1,"external_id":{"isi":["000485392800004"],"arxiv":["1309.2399"]},"language":[{"iso":"eng"}],"doi":"10.1002/jgt.22436","ec_funded":1,"publisher":"Wiley","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2019","volume":91,"date_updated":"2023-08-24T14:30:43Z","date_created":"2018-12-30T22:59:15Z","author":[{"full_name":"Chaplick, Steven","last_name":"Chaplick","first_name":"Steven"},{"last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","full_name":"Fulek, Radoslav"},{"last_name":"Klavík","first_name":"Pavel","full_name":"Klavík, Pavel"}],"scopus_import":"1","article_processing_charge":"No","day":"01","page":"365-394","article_type":"original","citation":{"mla":"Chaplick, Steven, et al. “Extending Partial Representations of Circle Graphs.” Journal of Graph Theory, vol. 91, no. 4, Wiley, 2019, pp. 365–94, doi:10.1002/jgt.22436.","short":"S. Chaplick, R. Fulek, P. Klavík, Journal of Graph Theory 91 (2019) 365–394.","chicago":"Chaplick, Steven, Radoslav Fulek, and Pavel Klavík. “Extending Partial Representations of Circle Graphs.” Journal of Graph Theory. Wiley, 2019. https://doi.org/10.1002/jgt.22436.","ama":"Chaplick S, Fulek R, Klavík P. Extending partial representations of circle graphs. Journal of Graph Theory. 2019;91(4):365-394. doi:10.1002/jgt.22436","ista":"Chaplick S, Fulek R, Klavík P. 2019. Extending partial representations of circle graphs. Journal of Graph Theory. 91(4), 365–394.","apa":"Chaplick, S., Fulek, R., & Klavík, P. (2019). Extending partial representations of circle graphs. Journal of Graph Theory. Wiley. https://doi.org/10.1002/jgt.22436","ieee":"S. Chaplick, R. Fulek, and P. Klavík, “Extending partial representations of circle graphs,” Journal of Graph Theory, vol. 91, no. 4. Wiley, pp. 365–394, 2019."},"publication":"Journal of Graph Theory","date_published":"2019-08-01T00:00:00Z","type":"journal_article","issue":"4","abstract":[{"text":"The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some predrawn chords that represent an induced subgraph of G. The question is whether one can extend R′ to a representation R of the entire graph G, that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of G. Our main result is an O(n3) time algorithm for partial representation extension of circle graphs, where n is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.","lang":"eng"}],"intvolume":" 91","title":"Extending partial representations of circle graphs","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"5790","oa_version":"Preprint"},{"month":"04","publication_identifier":{"issn":["0166218X"]},"external_id":{"isi":["000466061100020"],"arxiv":["1708.08037"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.08037"}],"quality_controlled":"1","isi":1,"project":[{"grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425","name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF"}],"doi":"10.1016/j.dam.2018.12.025","language":[{"iso":"eng"}],"year":"2019","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Elsevier","author":[{"full_name":"Fulek, Radoslav","last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pach","first_name":"János","full_name":"Pach, János"}],"related_material":{"record":[{"id":"433","relation":"earlier_version","status":"public"}]},"date_updated":"2023-08-24T14:39:33Z","date_created":"2019-01-20T22:59:17Z","volume":259,"scopus_import":"1","day":"30","article_processing_charge":"No","publication":"Discrete Applied Mathematics","citation":{"chicago":"Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” Discrete Applied Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.dam.2018.12.025.","mla":"Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” Discrete Applied Mathematics, vol. 259, no. 4, Elsevier, 2019, pp. 266–231, doi:10.1016/j.dam.2018.12.025.","short":"R. Fulek, J. Pach, Discrete Applied Mathematics 259 (2019) 266–231.","ista":"Fulek R, Pach J. 2019. Thrackles: An improved upper bound. Discrete Applied Mathematics. 259(4), 266–231.","apa":"Fulek, R., & Pach, J. (2019). Thrackles: An improved upper bound. Discrete Applied Mathematics. Elsevier. https://doi.org/10.1016/j.dam.2018.12.025","ieee":"R. Fulek and J. Pach, “Thrackles: An improved upper bound,” Discrete Applied Mathematics, vol. 259, no. 4. Elsevier, pp. 266–231, 2019.","ama":"Fulek R, Pach J. Thrackles: An improved upper bound. Discrete Applied Mathematics. 2019;259(4):266-231. doi:10.1016/j.dam.2018.12.025"},"article_type":"original","page":"266-231","date_published":"2019-04-30T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is [Formula presented](n−1), and that this bound is best possible for infinitely many values of n."}],"issue":"4","_id":"5857","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"Thrackles: An improved upper bound","intvolume":" 259","oa_version":"Preprint"},{"publisher":"Elsevier","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2019","volume":342,"date_updated":"2023-08-29T06:31:41Z","date_created":"2019-07-14T21:59:20Z","author":[{"first_name":"André ","last_name":"Silva","full_name":"Silva, André "},{"full_name":"Arroyo Guevara, Alan M","orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara","first_name":"Alan M"},{"first_name":"Bruce","last_name":"Richter","full_name":"Richter, Bruce"},{"full_name":"Lee, Orlando","first_name":"Orlando","last_name":"Lee"}],"ec_funded":1,"project":[{"_id":"26366136-B435-11E9-9278-68D0E5697425","name":"Reglas de Conectividad funcional en el hipocampo"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","isi":1,"external_id":{"arxiv":["1901.09955"],"isi":["000486358100025"]},"main_file_link":[{"url":"https://arxiv.org/abs/1901.09955","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.disc.2019.06.031","publication_identifier":{"issn":["0012-365X"]},"month":"11","intvolume":" 342","status":"public","title":"Graphs with at most one crossing","_id":"6638","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"journal_article","issue":"11","abstract":[{"text":"The crossing number of a graph G is the least number of crossings over all possible drawings of G. We present a structural characterization of graphs with crossing number one.","lang":"eng"}],"page":"3201-3207","citation":{"mla":"Silva, André, et al. “Graphs with at Most One Crossing.” Discrete Mathematics, vol. 342, no. 11, Elsevier, 2019, pp. 3201–07, doi:10.1016/j.disc.2019.06.031.","short":"A. Silva, A.M. Arroyo Guevara, B. Richter, O. Lee, Discrete Mathematics 342 (2019) 3201–3207.","chicago":"Silva, André , Alan M Arroyo Guevara, Bruce Richter, and Orlando Lee. “Graphs with at Most One Crossing.” Discrete Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.disc.2019.06.031.","ama":"Silva A, Arroyo Guevara AM, Richter B, Lee O. Graphs with at most one crossing. Discrete Mathematics. 2019;342(11):3201-3207. doi:10.1016/j.disc.2019.06.031","ista":"Silva A, Arroyo Guevara AM, Richter B, Lee O. 2019. Graphs with at most one crossing. Discrete Mathematics. 342(11), 3201–3207.","ieee":"A. Silva, A. M. Arroyo Guevara, B. Richter, and O. Lee, “Graphs with at most one crossing,” Discrete Mathematics, vol. 342, no. 11. Elsevier, pp. 3201–3207, 2019.","apa":"Silva, A., Arroyo Guevara, A. M., Richter, B., & Lee, O. (2019). Graphs with at most one crossing. Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.disc.2019.06.031"},"publication":"Discrete Mathematics","date_published":"2019-11-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01"},{"main_file_link":[{"url":"https://arxiv.org/abs/1709.00508","open_access":"1"}],"external_id":{"isi":["000493267200003"],"arxiv":["1709.00508"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"},{"_id":"261FA626-B435-11E9-9278-68D0E5697425","grant_number":"M02281","name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF"}],"doi":"10.1007/s00493-019-3905-7","language":[{"iso":"eng"}],"month":"10","publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"year":"2019","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","author":[{"full_name":"Fulek, Radoslav","first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774"},{"first_name":"Jan","last_name":"Kynčl","full_name":"Kynčl, Jan"}],"date_created":"2019-11-18T14:29:50Z","date_updated":"2023-08-30T07:26:25Z","volume":39,"ec_funded":1,"publication":"Combinatorica","citation":{"chicago":"Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” Combinatorica. Springer Nature, 2019. https://doi.org/10.1007/s00493-019-3905-7.","short":"R. Fulek, J. Kynčl, Combinatorica 39 (2019) 1267–1279.","mla":"Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” Combinatorica, vol. 39, no. 6, Springer Nature, 2019, pp. 1267–79, doi:10.1007/s00493-019-3905-7.","apa":"Fulek, R., & Kynčl, J. (2019). Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-019-3905-7","ieee":"R. Fulek and J. Kynčl, “Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4,” Combinatorica, vol. 39, no. 6. Springer Nature, pp. 1267–1279, 2019.","ista":"Fulek R, Kynčl J. 2019. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. 39(6), 1267–1279.","ama":"Fulek R, Kynčl J. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. 2019;39(6):1267-1279. doi:10.1007/s00493-019-3905-7"},"article_type":"original","page":"1267-1279","date_published":"2019-10-29T00:00:00Z","scopus_import":"1","day":"29","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7034","status":"public","title":"Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4","intvolume":" 39","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani–Tutte theorem cannot be extended to the orientable surface of genus 4. As a base step in the construction we use a counterexample to an extension of the unified Hanani–Tutte theorem on the torus."}],"issue":"6"},{"publication_identifier":{"issn":["0004-5411"]},"month":"06","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1711.08436.pdf"}],"external_id":{"arxiv":["1711.08436"],"isi":["000495406300007"]},"quality_controlled":"1","isi":1,"doi":"10.1145/3314024","language":[{"iso":"eng"}],"article_number":"21","year":"2019","department":[{"_id":"UlWa"}],"publisher":"ACM","publication_status":"published","related_material":{"record":[{"id":"184","status":"public","relation":"earlier_version"}]},"author":[{"last_name":"Goaoc","first_name":"Xavier","full_name":"Goaoc, Xavier"},{"first_name":"Pavel","last_name":"Patak","id":"B593B804-1035-11EA-B4F1-947645A5BB83","full_name":"Patak, Pavel"},{"full_name":"Patakova, Zuzana","first_name":"Zuzana","last_name":"Patakova","id":"48B57058-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3975-1683"},{"full_name":"Tancer, Martin","last_name":"Tancer","first_name":"Martin"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"volume":66,"date_created":"2019-11-26T10:13:59Z","date_updated":"2023-09-06T11:10:58Z","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"ama":"Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. Shellability is NP-complete. Journal of the ACM. 2019;66(3). doi:10.1145/3314024","ista":"Goaoc X, Patak P, Patakova Z, Tancer M, Wagner U. 2019. Shellability is NP-complete. Journal of the ACM. 66(3), 21.","apa":"Goaoc, X., Patak, P., Patakova, Z., Tancer, M., & Wagner, U. (2019). Shellability is NP-complete. Journal of the ACM. ACM. https://doi.org/10.1145/3314024","ieee":"X. Goaoc, P. Patak, Z. Patakova, M. Tancer, and U. Wagner, “Shellability is NP-complete,” Journal of the ACM, vol. 66, no. 3. ACM, 2019.","mla":"Goaoc, Xavier, et al. “Shellability Is NP-Complete.” Journal of the ACM, vol. 66, no. 3, 21, ACM, 2019, doi:10.1145/3314024.","short":"X. Goaoc, P. Patak, Z. Patakova, M. Tancer, U. Wagner, Journal of the ACM 66 (2019).","chicago":"Goaoc, Xavier, Pavel Patak, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Shellability Is NP-Complete.” Journal of the ACM. ACM, 2019. https://doi.org/10.1145/3314024."},"publication":"Journal of the ACM","article_type":"original","date_published":"2019-06-01T00:00:00Z","type":"journal_article","issue":"3","abstract":[{"lang":"eng","text":"We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes. Another simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-shellable."}],"_id":"7108","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":" 66","title":"Shellability is NP-complete","status":"public","oa_version":"Preprint"},{"scopus_import":"1","article_processing_charge":"No","day":"28","page":"230-243","citation":{"ista":"Arroyo Guevara AM, Derka M, Parada I. 2019. Extending simple drawings. 27th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 11904, 230–243.","apa":"Arroyo Guevara, A. M., Derka, M., & Parada, I. (2019). Extending simple drawings. In 27th International Symposium on Graph Drawing and Network Visualization (Vol. 11904, pp. 230–243). Prague, Czech Republic: Springer Nature. https://doi.org/10.1007/978-3-030-35802-0_18","ieee":"A. M. Arroyo Guevara, M. Derka, and I. Parada, “Extending simple drawings,” in 27th International Symposium on Graph Drawing and Network Visualization, Prague, Czech Republic, 2019, vol. 11904, pp. 230–243.","ama":"Arroyo Guevara AM, Derka M, Parada I. Extending simple drawings. In: 27th International Symposium on Graph Drawing and Network Visualization. Vol 11904. Springer Nature; 2019:230-243. doi:10.1007/978-3-030-35802-0_18","chicago":"Arroyo Guevara, Alan M, Martin Derka, and Irene Parada. “Extending Simple Drawings.” In 27th International Symposium on Graph Drawing and Network Visualization, 11904:230–43. Springer Nature, 2019. https://doi.org/10.1007/978-3-030-35802-0_18.","mla":"Arroyo Guevara, Alan M., et al. “Extending Simple Drawings.” 27th International Symposium on Graph Drawing and Network Visualization, vol. 11904, Springer Nature, 2019, pp. 230–43, doi:10.1007/978-3-030-35802-0_18.","short":"A.M. Arroyo Guevara, M. Derka, I. Parada, in:, 27th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2019, pp. 230–243."},"publication":"27th International Symposium on Graph Drawing and Network Visualization","date_published":"2019-11-28T00:00:00Z","alternative_title":["LNCS"],"type":"conference","abstract":[{"text":"Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing D(G) of a graph G by inserting a set of edges from the complement of G into D(G) such that the result is a simple drawing. In the context of rectilinear drawings, the problem is trivial. For pseudolinear drawings, the existence of such an extension follows from Levi’s enlargement lemma. In contrast, we prove that deciding if a given set of edges can be inserted into a simple drawing is NP-complete. Moreover, we show that the maximization version of the problem is APX-hard. We also present a polynomial-time algorithm for deciding whether one edge uv can be inserted into D(G) when {u,v} is a dominating set for the graph G.","lang":"eng"}],"intvolume":" 11904","title":"Extending simple drawings","status":"public","_id":"7230","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","publication_identifier":{"issn":["0302-9743"],"isbn":["978-3-0303-5801-3"],"eissn":["1611-3349"]},"month":"11","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"quality_controlled":"1","isi":1,"external_id":{"isi":["000612918800018"],"arxiv":["1908.08129"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1908.08129"}],"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-35802-0_18","conference":{"end_date":"2019-09-20","location":"Prague, Czech Republic","start_date":"2019-09-17","name":"GD: Graph Drawing and Network Visualization"},"ec_funded":1,"department":[{"_id":"UlWa"}],"publisher":"Springer Nature","publication_status":"published","year":"2019","volume":11904,"date_created":"2020-01-05T23:00:47Z","date_updated":"2023-09-06T14:56:00Z","author":[{"id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","first_name":"Alan M","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M"},{"first_name":"Martin","last_name":"Derka","full_name":"Derka, Martin"},{"full_name":"Parada, Irene","first_name":"Irene","last_name":"Parada"}]},{"article_processing_charge":"No","has_accepted_license":"1","day":"08","date_published":"2019-08-08T00:00:00Z","citation":{"chicago":"Zhechev, Stephan Y. “Algorithmic Aspects of Homotopy Theory and Embeddability.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:6681.","mla":"Zhechev, Stephan Y. Algorithmic Aspects of Homotopy Theory and Embeddability. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:6681.","short":"S.Y. Zhechev, Algorithmic Aspects of Homotopy Theory and Embeddability, Institute of Science and Technology Austria, 2019.","ista":"Zhechev SY. 2019. Algorithmic aspects of homotopy theory and embeddability. Institute of Science and Technology Austria.","apa":"Zhechev, S. Y. (2019). Algorithmic aspects of homotopy theory and embeddability. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:6681","ieee":"S. Y. Zhechev, “Algorithmic aspects of homotopy theory and embeddability,” Institute of Science and Technology Austria, 2019.","ama":"Zhechev SY. Algorithmic aspects of homotopy theory and embeddability. 2019. doi:10.15479/AT:ISTA:6681"},"page":"104","abstract":[{"lang":"eng","text":"The first part of the thesis considers the computational aspects of the homotopy groups πd(X) of a topological space X. It is well known that there is no algorithm to decide whether the fundamental group π1(X) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with π1(X) trivial), compute the higher homotopy group πd(X) for any given d ≥ 2.\r\nHowever, these algorithms come with a caveat: They compute the isomorphism type of πd(X), d ≥ 2 as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of πd(X). We present an algorithm that, given a simply connected space X, computes πd(X) and represents its elements as simplicial maps from suitable triangulations of the d-sphere Sd to X. For fixed d, the algorithm runs in time exponential in size(X), the number of simplices of X. Moreover, we prove that this is optimal: For every fixed d ≥ 2,\r\nwe construct a family of simply connected spaces X such that for any simplicial map representing a generator of πd(X), the size of the triangulation of S d on which the map is defined, is exponential in size(X).\r\nIn the second part of the thesis, we prove that the following question is algorithmically undecidable for d < ⌊3(k+1)/2⌋, k ≥ 5 and (k, d) ̸= (5, 7), which covers essentially everything outside the meta-stable range: Given a finite simplicial complex K of dimension k, decide whether there exists a piecewise-linear (i.e., linear on an arbitrarily fine subdivision of K) embedding f : K ↪→ Rd of K into a d-dimensional Euclidean space."}],"type":"dissertation","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","file":[{"creator":"szhechev","file_size":1464227,"content_type":"application/pdf","access_level":"open_access","file_name":"Stephan_Zhechev_thesis.pdf","checksum":"3231e7cbfca3b5687366f84f0a57a0c0","date_created":"2019-08-07T13:02:50Z","date_updated":"2020-07-14T12:47:37Z","file_id":"6771","relation":"main_file"},{"relation":"source_file","file_id":"6772","date_updated":"2020-07-14T12:47:37Z","date_created":"2019-08-07T13:03:22Z","checksum":"85d65eb27b4377a9e332ee37a70f08b6","file_name":"Stephan_Zhechev_thesis.tex","access_level":"closed","content_type":"application/octet-stream","file_size":303988,"creator":"szhechev"},{"creator":"szhechev","content_type":"application/zip","file_size":1087004,"access_level":"closed","file_name":"supplementary_material.zip","checksum":"86b374d264ca2dd53e712728e253ee75","date_updated":"2020-07-14T12:47:37Z","date_created":"2019-08-07T13:03:34Z","file_id":"6773","relation":"supplementary_material"}],"_id":"6681","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Algorithmic aspects of homotopy theory and embeddability","ddc":["514"],"publication_identifier":{"issn":["2663-337X"]},"month":"08","doi":"10.15479/AT:ISTA:6681","language":[{"iso":"eng"}],"supervisor":[{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli"}],"degree_awarded":"PhD","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"file_date_updated":"2020-07-14T12:47:37Z","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"6774"}]},"author":[{"full_name":"Zhechev, Stephan Y","last_name":"Zhechev","first_name":"Stephan Y","id":"3AA52972-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-09-07T13:10:36Z","date_created":"2019-07-26T11:14:34Z","year":"2019","publisher":"Institute of Science and Technology Austria","department":[{"_id":"UlWa"}],"publication_status":"published"},{"publisher":"arXiv","department":[{"_id":"UlWa"}],"publication_status":"submitted","status":"public","title":"Vanishing of all equivariant obstructions and the mapping degree","year":"2019","_id":"8182","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","date_created":"2020-07-30T10:45:08Z","date_updated":"2023-09-07T13:12:17Z","related_material":{"record":[{"status":"public","relation":"later_version","id":"11446"},{"relation":"dissertation_contains","status":"public","id":"8156"}]},"author":[{"full_name":"Avvakumov, Sergey","first_name":"Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kudrya, Sergey","last_name":"Kudrya","first_name":"Sergey","id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67"}],"type":"preprint","article_number":"1910.12628","abstract":[{"text":"Suppose that $n\\neq p^k$ and $n\\neq 2p^k$ for all $k$ and all primes $p$. We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $\\mathfrak S_n$ there exists an $\\mathfrak S_n$-equivariant map $X \\to\r\n{\\mathbb R}^n$ whose image avoids the diagonal $\\{(x,x\\dots,x)\\in {\\mathbb R}^n|x\\in {\\mathbb R}\\}$.\r\n Previously, the special cases of this statement for certain $X$ were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We\r\ntake a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of $\\mathfrak S_n$-equivariant maps from the boundary\r\n$\\partial\\Delta^{n-1}$ of $(n-1)$-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser's conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.","lang":"eng"}],"project":[{"name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF","grant_number":"P31312","_id":"26611F5C-B435-11E9-9278-68D0E5697425"}],"oa":1,"citation":{"ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv.","ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” arXiv. arXiv.","apa":"Avvakumov, S., & Kudrya, S. (n.d.). Vanishing of all equivariant obstructions and the mapping degree. arXiv. arXiv.","ista":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv, 1910.12628.","short":"S. Avvakumov, S. Kudrya, ArXiv (n.d.).","mla":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv, 1910.12628, arXiv.","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv. arXiv, n.d."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.12628"}],"external_id":{"arxiv":["1910.12628"]},"publication":"arXiv","language":[{"iso":"eng"}],"date_published":"2019-10-28T00:00:00Z","article_processing_charge":"No","month":"10","day":"28"},{"author":[{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"related_material":{"record":[{"id":"8156","status":"public","relation":"dissertation_contains"}],"link":[{"relation":"later_version","url":"https://doi.org/10.1112/mtk.12059"}]},"date_updated":"2023-09-07T13:12:17Z","date_created":"2020-07-30T10:45:51Z","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8185","year":"2019","title":"Envy-free division using mapping degree","status":"public","publication_status":"submitted","department":[{"_id":"UlWa"}],"abstract":[{"lang":"eng","text":"In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem) is a certain boundary condition.\r\n We follow Erel Segal-Halevi, Fr\\'ed\\'eric Meunier, and Shira Zerbib, and replace the boundary condition by another assumption, which has the economic meaning of possibility for a player to prefer an empty part in the segment\r\npartition problem. We solve the problem positively when $n$, the number of players that divide the segment, is a prime power, and we provide counterexamples for every $n$ which is not a prime power. We also provide counterexamples relevant to a wider class of fair or envy-free partition problems when $n$ is odd and not a prime power."}],"article_number":"1907.11183","type":"preprint","doi":"10.48550/arXiv.1907.11183","date_published":"2019-07-25T00:00:00Z","language":[{"iso":"eng"}],"publication":"arXiv","oa":1,"external_id":{"arxiv":["1907.11183"]},"citation":{"chicago":"Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1907.11183.","short":"S. Avvakumov, R. Karasev, ArXiv (n.d.).","mla":"Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, 1907.11183, doi:10.48550/arXiv.1907.11183.","apa":"Avvakumov, S., & Karasev, R. (n.d.). Envy-free division using mapping degree. arXiv. https://doi.org/10.48550/arXiv.1907.11183","ieee":"S. Avvakumov and R. Karasev, “Envy-free division using mapping degree,” arXiv. .","ista":"Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv, 1907.11183.","ama":"Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv. doi:10.48550/arXiv.1907.11183"},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1907.11183"}],"project":[{"grant_number":"P31312","_id":"26611F5C-B435-11E9-9278-68D0E5697425","name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF"}],"month":"07","day":"25","article_processing_charge":"No"},{"file_date_updated":"2020-07-14T12:47:14Z","volume":61,"date_updated":"2023-09-07T13:17:36Z","date_created":"2019-02-14T11:54:08Z","related_material":{"record":[{"id":"683","status":"public","relation":"earlier_version"},{"status":"public","relation":"dissertation_contains","id":"7944"}]},"author":[{"first_name":"Anna","last_name":"Lubiw","full_name":"Lubiw, Anna"},{"full_name":"Masárová, Zuzana","first_name":"Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"publisher":"Springer Nature","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2019","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.1007/s00454-018-0035-8","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","isi":1,"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1710.02741"],"isi":["000466130000009"]},"issue":"4","abstract":[{"text":"Given a triangulation of a point set in the plane, a flip deletes an edge e whose removal leaves a convex quadrilateral, and replaces e by the opposite diagonal of the quadrilateral. It is well known that any triangulation of a point set can be reconfigured to any other triangulation by some sequence of flips. We explore this question in the setting where each edge of a triangulation has a label, and a flip transfers the label of the removed edge to the new edge. It is not true that every labelled triangulation of a point set can be reconfigured to every other labelled triangulation via a sequence of flips, but we characterize when this is possible. There is an obvious necessary condition: for each label l, if edge e has label l in the first triangulation and edge f has label l in the second triangulation, then there must be some sequence of flips that moves label l from e to f, ignoring all other labels. Bose, Lubiw, Pathak and Verdonschot formulated the Orbit Conjecture, which states that this necessary condition is also sufficient, i.e. that all labels can be simultaneously mapped to their destination if and only if each label individually can be mapped to its destination. We prove this conjecture. Furthermore, we give a polynomial-time algorithm (with 𝑂(𝑛8) being a crude bound on the run-time) to find a sequence of flips to reconfigure one labelled triangulation to another, if such a sequence exists, and we prove an upper bound of 𝑂(𝑛7) on the length of the flip sequence. Our proof uses the topological result that the sets of pairwise non-crossing edges on a planar point set form a simplicial complex that is homeomorphic to a high-dimensional ball (this follows from a result of Orden and Santos; we give a different proof based on a shelling argument). The dual cell complex of this simplicial ball, called the flip complex, has the usual flip graph as its 1-skeleton. We use properties of the 2-skeleton of the flip complex to prove the Orbit Conjecture.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"file_id":"5988","relation":"main_file","checksum":"e1bff88f1d77001b53b78c485ce048d7","date_updated":"2020-07-14T12:47:14Z","date_created":"2019-02-14T11:57:22Z","access_level":"open_access","file_name":"2018_DiscreteGeometry_Lubiw.pdf","creator":"dernst","content_type":"application/pdf","file_size":556276}],"intvolume":" 61","status":"public","title":"A proof of the orbit conjecture for flipping edge-labelled triangulations","ddc":["000"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"5986","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2019-06-01T00:00:00Z","page":"880-898","article_type":"original","citation":{"short":"A. Lubiw, Z. Masárová, U. Wagner, Discrete & Computational Geometry 61 (2019) 880–898.","mla":"Lubiw, Anna, et al. “A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations.” Discrete & Computational Geometry, vol. 61, no. 4, Springer Nature, 2019, pp. 880–98, doi:10.1007/s00454-018-0035-8.","chicago":"Lubiw, Anna, Zuzana Masárová, and Uli Wagner. “A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations.” Discrete & Computational Geometry. Springer Nature, 2019. https://doi.org/10.1007/s00454-018-0035-8.","ama":"Lubiw A, Masárová Z, Wagner U. A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. 2019;61(4):880-898. doi:10.1007/s00454-018-0035-8","ieee":"A. Lubiw, Z. Masárová, and U. Wagner, “A proof of the orbit conjecture for flipping edge-labelled triangulations,” Discrete & Computational Geometry, vol. 61, no. 4. Springer Nature, pp. 880–898, 2019.","apa":"Lubiw, A., Masárová, Z., & Wagner, U. (2019). A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-018-0035-8","ista":"Lubiw A, Masárová Z, Wagner U. 2019. A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. 61(4), 880–898."},"publication":"Discrete & Computational Geometry"},{"date_published":"2019-06-01T00:00:00Z","page":"44:1-44:20","citation":{"chicago":"Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small Treewidth.” In 35th International Symposium on Computational Geometry, 129:44:1-44:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPIcs.SoCG.2019.44.","mla":"Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small Treewidth.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20, doi:10.4230/LIPIcs.SoCG.2019.44.","short":"K. Huszár, J. Spreer, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20.","ista":"Huszár K, Spreer J. 2019. 3-manifold triangulations with small treewidth. 35th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 129, 44:1-44:20.","apa":"Huszár, K., & Spreer, J. (2019). 3-manifold triangulations with small treewidth. In 35th International Symposium on Computational Geometry (Vol. 129, p. 44:1-44:20). Portland, Oregon, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2019.44","ieee":"K. Huszár and J. Spreer, “3-manifold triangulations with small treewidth,” in 35th International Symposium on Computational Geometry, Portland, Oregon, United States, 2019, vol. 129, p. 44:1-44:20.","ama":"Huszár K, Spreer J. 3-manifold triangulations with small treewidth. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:44:1-44:20. doi:10.4230/LIPIcs.SoCG.2019.44"},"publication":"35th International Symposium on Computational Geometry","has_accepted_license":"1","article_processing_charge":"No","day":"01","keyword":["computational 3-manifold topology","fixed-parameter tractability","layered triangulations","structural graph theory","treewidth","cutwidth","Heegaard genus"],"scopus_import":"1","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2019_LIPIcs-Huszar.pdf","creator":"kschuh","file_size":905885,"content_type":"application/pdf","file_id":"6557","relation":"main_file","checksum":"29d18c435368468aa85823dabb157e43","date_created":"2019-06-12T06:45:33Z","date_updated":"2020-07-14T12:47:33Z"}],"intvolume":" 129","status":"public","ddc":["516"],"title":"3-manifold triangulations with small treewidth","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6556","abstract":[{"text":"Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined to be the minimum treewidth of the face pairing graph of any triangulation T of M. In this setting the relationship between the topology of a 3-manifold and its treewidth is of particular interest. First, as a corollary of work of Jaco and Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination with our earlier work with Wagner, this yields that for non-Haken manifolds the Heegaard genus and the treewidth are within a constant factor. Second, we characterize all 3-manifolds of treewidth one: These are precisely the lens spaces and a single other Seifert fibered space. Furthermore, we show that all remaining orientable Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth two. In particular, for every spherical 3-manifold we exhibit a triangulation of treewidth at most two. Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing FPT-algorithms in the field.","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2019.44","conference":{"end_date":"2019-06-21","location":"Portland, Oregon, United States","start_date":"2019-06-18","name":"SoCG: Symposium on Computational Geometry"},"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["1812.05528"]},"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-104-7"]},"month":"06","volume":129,"date_updated":"2023-09-07T13:18:26Z","date_created":"2019-06-11T20:09:57Z","related_material":{"record":[{"id":"8032","relation":"part_of_dissertation","status":"public"}]},"author":[{"full_name":"Huszár, Kristóf","orcid":"0000-0002-5445-5057","id":"33C26278-F248-11E8-B48F-1D18A9856A87","last_name":"Huszár","first_name":"Kristóf"},{"last_name":"Spreer","first_name":"Jonathan","full_name":"Spreer, Jonathan"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2019","file_date_updated":"2020-07-14T12:47:33Z"},{"ddc":["514"],"status":"public","title":"On the treewidth of triangulated 3-manifolds","intvolume":" 10","_id":"7093","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Published Version","file":[{"checksum":"c872d590d38d538404782bca20c4c3f5","date_updated":"2020-07-14T12:47:49Z","date_created":"2019-11-23T12:35:16Z","file_id":"7094","relation":"main_file","creator":"khuszar","file_size":857590,"content_type":"application/pdf","access_level":"open_access","file_name":"479-1917-1-PB.pdf"}],"type":"journal_article","abstract":[{"text":"In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how \"simple\" or \"thin\" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth.\r\nIn view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs).\r\nWe derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 18(k+1) (resp. 4(3k+1)).","lang":"eng"}],"issue":"2","article_type":"original","page":"70–98","publication":"Journal of Computational Geometry","citation":{"ista":"Huszár K, Spreer J, Wagner U. 2019. On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. 10(2), 70–98.","ieee":"K. Huszár, J. Spreer, and U. Wagner, “On the treewidth of triangulated 3-manifolds,” Journal of Computational Geometry, vol. 10, no. 2. Computational Geometry Laborartoy, pp. 70–98, 2019.","apa":"Huszár, K., Spreer, J., & Wagner, U. (2019). On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. Computational Geometry Laborartoy. https://doi.org/10.20382/JOGC.V10I2A5","ama":"Huszár K, Spreer J, Wagner U. On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. 2019;10(2):70–98. doi:10.20382/JOGC.V10I2A5","chicago":"Huszár, Kristóf, Jonathan Spreer, and Uli Wagner. “On the Treewidth of Triangulated 3-Manifolds.” Journal of Computational Geometry. Computational Geometry Laborartoy, 2019. https://doi.org/10.20382/JOGC.V10I2A5.","mla":"Huszár, Kristóf, et al. “On the Treewidth of Triangulated 3-Manifolds.” Journal of Computational Geometry, vol. 10, no. 2, Computational Geometry Laborartoy, 2019, pp. 70–98, doi:10.20382/JOGC.V10I2A5.","short":"K. Huszár, J. Spreer, U. Wagner, Journal of Computational Geometry 10 (2019) 70–98."},"date_published":"2019-11-01T00:00:00Z","day":"01","has_accepted_license":"1","article_processing_charge":"No","publication_status":"published","publisher":"Computational Geometry Laborartoy","department":[{"_id":"UlWa"}],"year":"2019","date_created":"2019-11-23T12:14:09Z","date_updated":"2023-09-07T13:18:26Z","volume":10,"author":[{"full_name":"Huszár, Kristóf","last_name":"Huszár","first_name":"Kristóf","orcid":"0000-0002-5445-5057","id":"33C26278-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Spreer, Jonathan","first_name":"Jonathan","last_name":"Spreer"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"285"},{"relation":"part_of_dissertation","status":"public","id":"8032"}]},"file_date_updated":"2020-07-14T12:47:49Z","quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1712.00434"]},"language":[{"iso":"eng"}],"doi":"10.20382/JOGC.V10I2A5","month":"11","publication_identifier":{"issn":["1920-180X"]}},{"publication_status":"submitted","title":"Stronger counterexamples to the topological Tverberg conjecture","status":"public","department":[{"_id":"UlWa"}],"publisher":"arXiv","_id":"8184","acknowledgement":"We would like to thank F. Frick for helpful discussions","year":"2019","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2023-09-08T11:20:02Z","date_created":"2020-07-30T10:45:34Z","oa_version":"Preprint","author":[{"first_name":"Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey"},{"full_name":"Karasev, R.","last_name":"Karasev","first_name":"R."},{"full_name":"Skopenkov, A.","last_name":"Skopenkov","first_name":"A."}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"8156"}]},"article_number":"1908.08731","type":"preprint","abstract":[{"text":"Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if r is not a prime power and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional counterexamples by taking k-fold join power of lower-dimensional ones. We improve this further (for d large compared to r): If r is not a prime power and N := (d+ 1)r−r l\r\nd + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the r-fold van Kampen–Flores conjecture we also produce counterexamples which are stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner theorem on construction of almost r-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariant maps. ","lang":"eng"}],"isi":1,"project":[{"call_identifier":"FWF","name":"Algorithms for Embeddings and Homotopy Theory","_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312"}],"publication":"arXiv","external_id":{"isi":["000986519600004"],"arxiv":["1908.08731"]},"citation":{"chicago":"Avvakumov, Sergey, R. Karasev, and A. Skopenkov. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv. arXiv, n.d.","short":"S. Avvakumov, R. Karasev, A. Skopenkov, ArXiv (n.d.).","mla":"Avvakumov, Sergey, et al. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv, 1908.08731, arXiv.","ieee":"S. Avvakumov, R. Karasev, and A. Skopenkov, “Stronger counterexamples to the topological Tverberg conjecture,” arXiv. arXiv.","apa":"Avvakumov, S., Karasev, R., & Skopenkov, A. (n.d.). Stronger counterexamples to the topological Tverberg conjecture. arXiv. arXiv.","ista":"Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv, 1908.08731.","ama":"Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv."},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1908.08731","open_access":"1"}],"language":[{"iso":"eng"}],"date_published":"2019-08-23T00:00:00Z","day":"23","month":"08","article_processing_charge":"No"},{"volume":15,"date_created":"2019-11-04T15:45:17Z","date_updated":"2023-09-15T12:19:31Z","related_material":{"record":[{"id":"309","relation":"earlier_version","status":"public"}]},"author":[{"last_name":"Akitaya","first_name":"Hugo","full_name":"Akitaya, Hugo"},{"last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","full_name":"Fulek, Radoslav"},{"last_name":"Tóth","first_name":"Csaba","full_name":"Tóth, Csaba"}],"publisher":"ACM","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2019","article_number":"50","language":[{"iso":"eng"}],"doi":"10.1145/3344549","project":[{"name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF","grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"external_id":{"arxiv":["1709.09209"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.09209"}],"month":"10","oa_version":"Preprint","intvolume":" 15","title":"Recognizing weak embeddings of graphs","status":"public","_id":"6982","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"4","abstract":[{"text":"We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding ϕ : G → M of a graph G into a 2-manifold M maps the vertices in V(G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to the same point or overlapping arcs due to data compression or low resolution. This raises the computational problem of deciding whether a given map ϕ : G → M comes from an embedding. A map ϕ : G → M is a weak embedding if it can be perturbed into an embedding ψ ϵ : G → M with ‖ ϕ − ψ ϵ ‖ < ϵ for every ϵ > 0, where ‖.‖ is the unform norm.\r\nA polynomial-time algorithm for recognizing weak embeddings has recently been found by Fulek and Kynčl. It reduces the problem to solving a system of linear equations over Z2. It runs in O(n2ω)≤ O(n4.75) time, where ω ∈ [2,2.373) is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler: We perform a sequence of local operations that gradually “untangles” the image ϕ(G) into an embedding ψ(G) or reports that ϕ is not a weak embedding. It combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.\r\n","lang":"eng"}],"type":"journal_article","date_published":"2019-10-01T00:00:00Z","article_type":"original","citation":{"chicago":"Akitaya, Hugo, Radoslav Fulek, and Csaba Tóth. “Recognizing Weak Embeddings of Graphs.” ACM Transactions on Algorithms. ACM, 2019. https://doi.org/10.1145/3344549.","mla":"Akitaya, Hugo, et al. “Recognizing Weak Embeddings of Graphs.” ACM Transactions on Algorithms, vol. 15, no. 4, 50, ACM, 2019, doi:10.1145/3344549.","short":"H. Akitaya, R. Fulek, C. Tóth, ACM Transactions on Algorithms 15 (2019).","ista":"Akitaya H, Fulek R, Tóth C. 2019. Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. 15(4), 50.","apa":"Akitaya, H., Fulek, R., & Tóth, C. (2019). Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. ACM. https://doi.org/10.1145/3344549","ieee":"H. Akitaya, R. Fulek, and C. Tóth, “Recognizing weak embeddings of graphs,” ACM Transactions on Algorithms, vol. 15, no. 4. ACM, 2019.","ama":"Akitaya H, Fulek R, Tóth C. Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. 2019;15(4). doi:10.1145/3344549"},"publication":"ACM Transactions on Algorithms","day":"01","scopus_import":1},{"project":[{"grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425","name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["1812.04911"]},"language":[{"iso":"eng"}],"doi":"10.4230/LIPICS.SOCG.2019.38","conference":{"end_date":"2019-06-21","start_date":"2019-06-18","location":"Portland, OR, United States","name":"SoCG 2019: Symposium on Computational Geometry"},"publication_identifier":{"isbn":["9783959771047"],"issn":["1868-8969"]},"month":"06","department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","year":"2019","volume":129,"date_updated":"2023-12-13T12:03:35Z","date_created":"2019-07-17T10:35:04Z","related_material":{"record":[{"id":"13974","status":"public","relation":"later_version"}]},"author":[{"last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","full_name":"Fulek, Radoslav"},{"first_name":"Bernd","last_name":"Gärtner","full_name":"Gärtner, Bernd"},{"last_name":"Kupavskii","first_name":"Andrey","full_name":"Kupavskii, Andrey"},{"full_name":"Valtr, Pavel","last_name":"Valtr","first_name":"Pavel"},{"full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"}],"file_date_updated":"2020-07-14T12:47:35Z","page":"38:1-38:13","citation":{"apa":"Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., & Wagner, U. (2019). The crossing Tverberg theorem. In 35th International Symposium on Computational Geometry (Vol. 129, p. 38:1-38:13). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.38","ieee":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing Tverberg theorem,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 38:1-38:13.","ista":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2019. The crossing Tverberg theorem. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 38:1-38:13.","ama":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:38:1-38:13. doi:10.4230/LIPICS.SOCG.2019.38","chicago":"Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner. “The Crossing Tverberg Theorem.” In 35th International Symposium on Computational Geometry, 129:38:1-38:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.38.","short":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 38:1-38:13.","mla":"Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 38:1-38:13, doi:10.4230/LIPICS.SOCG.2019.38."},"publication":"35th International Symposium on Computational Geometry","date_published":"2019-06-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01","intvolume":" 129","status":"public","title":"The crossing Tverberg theorem","ddc":["000","510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6647","file":[{"file_name":"2019_LIPICS_Fulek.pdf","access_level":"open_access","creator":"dernst","file_size":559837,"content_type":"application/pdf","file_id":"6667","relation":"main_file","date_created":"2019-07-24T06:54:52Z","date_updated":"2020-07-14T12:47:35Z","checksum":"d6d017f8b41291b94d102294fa96ae9c"}],"oa_version":"Published Version","alternative_title":["LIPIcs"],"type":"conference","abstract":[{"text":"The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r-1)+1 points in R^d, one can find a partition X=X_1 cup ... cup X_r of X, such that the convex hulls of the X_i, i=1,...,r, all share a common point. In this paper, we prove a strengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span floor[n/3] vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Alvarez-Rebollar et al. guarantees floor[n/6] pairwise crossing triangles. Our result generalizes to a result about simplices in R^d,d >=2.","lang":"eng"}]},{"publication":"arXiv","citation":{"ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","ieee":"A. Biniaz et al., “Token swapping on trees,” arXiv. .","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv.","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d.","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.)."},"oa":1,"external_id":{"arxiv":["1903.06981"]},"main_file_link":[{"url":"https://arxiv.org/abs/1903.06981","open_access":"1"}],"language":[{"iso":"eng"}],"date_published":"2019-03-16T00:00:00Z","day":"16","month":"03","article_processing_charge":"No","status":"public","publication_status":"submitted","title":"Token swapping on trees","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7950","year":"2019","date_updated":"2024-01-04T12:42:08Z","date_created":"2020-06-08T12:25:25Z","oa_version":"Preprint","author":[{"full_name":"Biniaz, Ahmad","last_name":"Biniaz","first_name":"Ahmad"},{"first_name":"Kshitij","last_name":"Jain","full_name":"Jain, Kshitij"},{"full_name":"Lubiw, Anna","last_name":"Lubiw","first_name":"Anna"},{"last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana"},{"full_name":"Miltzow, Tillmann","first_name":"Tillmann","last_name":"Miltzow"},{"first_name":"Debajyoti","last_name":"Mondal","full_name":"Mondal, Debajyoti"},{"full_name":"Naredla, Anurag Murty","first_name":"Anurag Murty","last_name":"Naredla"},{"full_name":"Tkadlec, Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","first_name":"Josef","last_name":"Tkadlec"},{"first_name":"Alexi","last_name":"Turcotte","full_name":"Turcotte, Alexi"}],"related_material":{"record":[{"id":"7944","status":"public","relation":"dissertation_contains"},{"relation":"later_version","status":"public","id":"12833"}]},"article_number":"1903.06981","type":"preprint","abstract":[{"text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.","lang":"eng"}]},{"publist_id":"7735","file_date_updated":"2020-07-14T12:45:19Z","article_number":"39","author":[{"full_name":"Fulek, Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","first_name":"Radoslav","last_name":"Fulek"},{"last_name":"Kynčl","first_name":"Jan","full_name":"Kynčl, Jan"}],"volume":99,"date_created":"2018-12-11T11:45:04Z","date_updated":"2021-01-12T06:53:36Z","year":"2018","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"publication_status":"published","publication_identifier":{"isbn":["978-3-95977-066-8"]},"month":"01","doi":"10.4230/LIPIcs.SoCG.2018.39","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11"},"language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425","name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"We resolve in the affirmative conjectures of A. Skopenkov and Repovš (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings. Our proof of this result is constructive and almost immediately implies an efficient algorithm for testing whether a given piecewise linear map of a graph in a surface is approximable by an embedding. More precisely, an instance of this problem consists of (i) a graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact surface M given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise disjoint "pipes" corresponding to the bundles, connecting certain pairs of these discs. We are to decide whether G can be embedded inside M so that the vertices in every cluster are drawn in the corresponding disc, the edges in every bundle pass only through its corresponding pipe, and every edge crosses the boundary of each disc at most once."}],"type":"conference","alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"oa_version":"Published Version","file":[{"date_created":"2018-12-17T12:33:52Z","date_updated":"2020-07-14T12:45:19Z","checksum":"f1b94f1a75b37c414a1f61d59fb2cd4c","file_id":"5701","relation":"main_file","creator":"dernst","file_size":718857,"content_type":"application/pdf","file_name":"2018_LIPIcs_Fulek.pdf","access_level":"open_access"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"185","intvolume":" 99","ddc":["510"],"status":"public","title":"Hanani-Tutte for approximating maps of graphs","has_accepted_license":"1","day":"01","scopus_import":1,"date_published":"2018-01-01T00:00:00Z","citation":{"ama":"Fulek R, Kynčl J. Hanani-Tutte for approximating maps of graphs. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.39","ista":"Fulek R, Kynčl J. 2018. Hanani-Tutte for approximating maps of graphs. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 39.","ieee":"R. Fulek and J. Kynčl, “Hanani-Tutte for approximating maps of graphs,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.","apa":"Fulek, R., & Kynčl, J. (2018). Hanani-Tutte for approximating maps of graphs (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.39","mla":"Fulek, Radoslav, and Jan Kynčl. Hanani-Tutte for Approximating Maps of Graphs. Vol. 99, 39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.39.","short":"R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","chicago":"Fulek, Radoslav, and Jan Kynčl. “Hanani-Tutte for Approximating Maps of Graphs,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.39."}},{"date_published":"2018-06-11T00:00:00Z","citation":{"short":"R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 40.1-40.14.","mla":"Fulek, Radoslav, and Jan Kynčl. The ℤ2-Genus of Kuratowski Minors. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 40.1-40.14, doi:10.4230/LIPIcs.SoCG.2018.40.","chicago":"Fulek, Radoslav, and Jan Kynčl. “The ℤ2-Genus of Kuratowski Minors,” 99:40.1-40.14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.40.","ama":"Fulek R, Kynčl J. The ℤ2-Genus of Kuratowski minors. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:40.1-40.14. doi:10.4230/LIPIcs.SoCG.2018.40","apa":"Fulek, R., & Kynčl, J. (2018). The ℤ2-Genus of Kuratowski minors (Vol. 99, p. 40.1-40.14). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.40","ieee":"R. Fulek and J. Kynčl, “The ℤ2-Genus of Kuratowski minors,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 40.1-40.14.","ista":"Fulek R, Kynčl J. 2018. The ℤ2-Genus of Kuratowski minors. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 40.1-40.14."},"page":"40.1 - 40.14","day":"11","article_processing_charge":"No","scopus_import":"1","oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"186","title":"The ℤ2-Genus of Kuratowski minors","status":"public","intvolume":" 99","abstract":[{"lang":"eng","text":"A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The ℤ2-genus of a graph G is the minimum g such that G has an independently even drawing on the orientable surface of genus g. An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a minor a projective t × t grid or one of the following so-called t-Kuratowski graphs: K3, t, or t copies of K5 or K3,3 sharing at most 2 common vertices. We show that the ℤ2-genus of graphs in these families is unbounded in t; in fact, equal to their genus. Together, this implies that the genus of a graph is bounded from above by a function of its ℤ2-genus, solving a problem posed by Schaefer and Štefankovič, and giving an approximate version of the Hanani-Tutte theorem on orientable surfaces."}],"type":"conference","alternative_title":["LIPIcs"],"conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2018-06-11","location":"Budapest, Hungary","end_date":"2018-06-14"},"doi":"10.4230/LIPIcs.SoCG.2018.40","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1803.05085","open_access":"1"}],"external_id":{"arxiv":["1803.05085"]},"oa":1,"quality_controlled":"1","project":[{"grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs"}],"month":"06","author":[{"orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek","first_name":"Radoslav","full_name":"Fulek, Radoslav"},{"full_name":"Kynčl, Jan","last_name":"Kynčl","first_name":"Jan"}],"related_material":{"record":[{"id":"11593","relation":"later_version","status":"public"}]},"date_updated":"2023-08-14T12:43:51Z","date_created":"2018-12-11T11:45:05Z","volume":99,"year":"2018","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publist_id":"7734"},{"month":"01","quality_controlled":"1","external_id":{"arxiv":["1708.08037"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.08037"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-73915-1_14","conference":{"location":"Boston, MA, United States","start_date":"201-09-25","end_date":"2017-09-27","name":"GD 2017: Graph Drawing and Network Visualization"},"publist_id":"7390","publisher":"Springer","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2018","volume":10692,"date_created":"2018-12-11T11:46:27Z","date_updated":"2023-08-24T14:39:32Z","related_material":{"record":[{"id":"5857","status":"public","relation":"later_version"}]},"author":[{"last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","full_name":"Fulek, Radoslav"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János"}],"scopus_import":1,"day":"21","page":"160 - 166","citation":{"ieee":"R. Fulek and J. Pach, “Thrackles: An improved upper bound,” presented at the GD 2017: Graph Drawing and Network Visualization, Boston, MA, United States, 2018, vol. 10692, pp. 160–166.","apa":"Fulek, R., & Pach, J. (2018). Thrackles: An improved upper bound (Vol. 10692, pp. 160–166). Presented at the GD 2017: Graph Drawing and Network Visualization, Boston, MA, United States: Springer. https://doi.org/10.1007/978-3-319-73915-1_14","ista":"Fulek R, Pach J. 2018. Thrackles: An improved upper bound. GD 2017: Graph Drawing and Network Visualization, LNCS, vol. 10692, 160–166.","ama":"Fulek R, Pach J. Thrackles: An improved upper bound. In: Vol 10692. Springer; 2018:160-166. doi:10.1007/978-3-319-73915-1_14","chicago":"Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound,” 10692:160–66. Springer, 2018. https://doi.org/10.1007/978-3-319-73915-1_14.","short":"R. Fulek, J. Pach, in:, Springer, 2018, pp. 160–166.","mla":"Fulek, Radoslav, and János Pach. Thrackles: An Improved Upper Bound. Vol. 10692, Springer, 2018, pp. 160–66, doi:10.1007/978-3-319-73915-1_14."},"date_published":"2018-01-21T00:00:00Z","alternative_title":["LNCS"],"type":"conference","abstract":[{"text":"A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is 3/2(n-1), and that this bound is best possible for infinitely many values of n.","lang":"eng"}],"intvolume":" 10692","status":"public","title":"Thrackles: An improved upper bound","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"433","oa_version":"Submitted Version"},{"citation":{"short":"X. Goaoc, P. Paták, Z. Patakova, M. Tancer, U. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 41:1-41:16.","mla":"Goaoc, Xavier, et al. Shellability Is NP-Complete. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 41:1-41:16, doi:10.4230/LIPIcs.SoCG.2018.41.","chicago":"Goaoc, Xavier, Pavel Paták, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Shellability Is NP-Complete,” 99:41:1-41:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.41.","ama":"Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. Shellability is NP-complete. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:41:1-41:16. doi:10.4230/LIPIcs.SoCG.2018.41","ieee":"X. Goaoc, P. Paták, Z. Patakova, M. Tancer, and U. Wagner, “Shellability is NP-complete,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 41:1-41:16.","apa":"Goaoc, X., Paták, P., Patakova, Z., Tancer, M., & Wagner, U. (2018). Shellability is NP-complete (Vol. 99, p. 41:1-41:16). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.41","ista":"Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. 2018. Shellability is NP-complete. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 41:1-41:16."},"page":"41:1 - 41:16","date_published":"2018-06-11T00:00:00Z","scopus_import":1,"day":"11","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"184","status":"public","title":"Shellability is NP-complete","ddc":["516","000"],"intvolume":" 99","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2018_LIPIcs_Goaoc.pdf","creator":"dernst","content_type":"application/pdf","file_size":718414,"file_id":"5725","relation":"main_file","checksum":"d12bdd60f04a57307867704b5f930afd","date_updated":"2020-07-14T12:45:18Z","date_created":"2018-12-17T16:35:02Z"}],"type":"conference","alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"abstract":[{"text":"We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","conference":{"end_date":"2018-06-14","start_date":"2018-06-11","location":"Budapest, Hungary","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2018.41","language":[{"iso":"eng"}],"month":"06","year":"2018","acknowledgement":"Partially supported by the project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM) of Czech-French collaboration.","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"author":[{"first_name":"Xavier","last_name":"Goaoc","full_name":"Goaoc, Xavier"},{"first_name":"Pavel","last_name":"Paták","full_name":"Paták, Pavel"},{"full_name":"Patakova, Zuzana","orcid":"0000-0002-3975-1683","id":"48B57058-F248-11E8-B48F-1D18A9856A87","last_name":"Patakova","first_name":"Zuzana"},{"id":"38AC689C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1191-6714","first_name":"Martin","last_name":"Tancer","full_name":"Tancer, Martin"},{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"}],"related_material":{"record":[{"id":"7108","status":"public","relation":"later_version"}]},"date_updated":"2023-09-06T11:10:57Z","date_created":"2018-12-11T11:45:04Z","volume":99,"file_date_updated":"2020-07-14T12:45:18Z","publist_id":"7736"},{"date_published":"2018-06-01T00:00:00Z","citation":{"mla":"Huszár, Kristóf, et al. On the Treewidth of Triangulated 3-Manifolds. Vol. 99, 46, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.46.","short":"K. Huszár, J. Spreer, U. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","chicago":"Huszár, Kristóf, Jonathan Spreer, and Uli Wagner. “On the Treewidth of Triangulated 3-Manifolds,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.46.","ama":"Huszár K, Spreer J, Wagner U. On the treewidth of triangulated 3-manifolds. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.46","ista":"Huszár K, Spreer J, Wagner U. 2018. On the treewidth of triangulated 3-manifolds. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 46.","ieee":"K. Huszár, J. Spreer, and U. Wagner, “On the treewidth of triangulated 3-manifolds,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.","apa":"Huszár, K., Spreer, J., & Wagner, U. (2018). On the treewidth of triangulated 3-manifolds (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.46"},"day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":1,"file":[{"date_updated":"2020-07-14T12:45:51Z","date_created":"2018-12-17T15:32:38Z","checksum":"530d084116778135d5bffaa317479cac","relation":"main_file","file_id":"5713","file_size":642522,"content_type":"application/pdf","creator":"dernst","file_name":"2018_LIPIcs_Huszar.pdf","access_level":"open_access"}],"oa_version":"Submitted Version","_id":"285","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["516","000"],"title":"On the treewidth of triangulated 3-manifolds","intvolume":" 99","abstract":[{"text":"In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth. In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs). We derive these results from work of Agol and of Scharlemann and Thompson, by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 48(k+1) (resp. 4(3k+1)).","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"conference":{"location":"Budapest, Hungary","start_date":"2018-06-11","end_date":"2018-06-14","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2018.46","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1712.00434"]},"quality_controlled":"1","month":"06","publication_identifier":{"issn":["18688969"]},"author":[{"full_name":"Huszár, Kristóf","last_name":"Huszár","first_name":"Kristóf","orcid":"0000-0002-5445-5057","id":"33C26278-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Spreer, Jonathan","last_name":"Spreer","first_name":"Jonathan"},{"first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli"}],"related_material":{"record":[{"id":"7093","relation":"later_version","status":"public"}]},"date_updated":"2023-09-06T11:13:41Z","date_created":"2018-12-11T11:45:37Z","volume":99,"acknowledgement":"Research of the second author was supported by the Einstein Foundation (project “Einstein Visiting Fellow Santos”) and by the Simons Foundation (“Simons Visiting Professors” program).","year":"2018","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"file_date_updated":"2020-07-14T12:45:51Z","publist_id":"7614","article_number":"46"},{"file_date_updated":"2020-07-14T12:47:40Z","date_updated":"2023-09-07T13:10:36Z","date_created":"2019-08-08T06:47:40Z","volume":2,"author":[{"id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Filakovský","full_name":"Filakovský, Marek"},{"full_name":"Franek, Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8878-8397","first_name":"Peter","last_name":"Franek"},{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"},{"first_name":"Stephan Y","last_name":"Zhechev","id":"3AA52972-F248-11E8-B48F-1D18A9856A87","full_name":"Zhechev, Stephan Y"}],"related_material":{"record":[{"id":"6681","relation":"dissertation_contains","status":"public"}]},"publication_status":"published","publisher":"Springer","department":[{"_id":"UlWa"}],"year":"2018","month":"12","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"language":[{"iso":"eng"}],"doi":"10.1007/s41468-018-0021-5","quality_controlled":"1","project":[{"name":"Robust invariants of Nonlinear Systems","call_identifier":"FWF","grant_number":"M01980","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"FWF Open Access Fund","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"abstract":[{"lang":"eng","text":"A central problem of algebraic topology is to understand the homotopy groups 𝜋𝑑(𝑋) of a topological space X. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental group 𝜋1(𝑋) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with 𝜋1(𝑋) trivial), compute the higher homotopy group 𝜋𝑑(𝑋) for any given 𝑑≥2 . However, these algorithms come with a caveat: They compute the isomorphism type of 𝜋𝑑(𝑋) , 𝑑≥2 as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of 𝜋𝑑(𝑋) . Converting elements of this abstract group into explicit geometric maps from the d-dimensional sphere 𝑆𝑑 to X has been one of the main unsolved problems in the emerging field of computational homotopy theory. Here we present an algorithm that, given a simply connected space X, computes 𝜋𝑑(𝑋) and represents its elements as simplicial maps from a suitable triangulation of the d-sphere 𝑆𝑑 to X. For fixed d, the algorithm runs in time exponential in size(𝑋) , the number of simplices of X. Moreover, we prove that this is optimal: For every fixed 𝑑≥2 , we construct a family of simply connected spaces X such that for any simplicial map representing a generator of 𝜋𝑑(𝑋) , the size of the triangulation of 𝑆𝑑 on which the map is defined, is exponential in size(𝑋) ."}],"issue":"3-4","type":"journal_article","oa_version":"Published Version","file":[{"checksum":"cf9e7fcd2a113dd4828774fc75cdb7e8","date_updated":"2020-07-14T12:47:40Z","date_created":"2019-08-08T06:55:21Z","relation":"main_file","file_id":"6775","content_type":"application/pdf","file_size":1056278,"creator":"dernst","access_level":"open_access","file_name":"2018_JourAppliedComputTopology_Filakovsky.pdf"}],"ddc":["514"],"status":"public","title":"Computing simplicial representatives of homotopy group elements","intvolume":" 2","_id":"6774","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","has_accepted_license":"1","date_published":"2018-12-01T00:00:00Z","article_type":"original","page":"177-231","publication":"Journal of Applied and Computational Topology","citation":{"short":"M. Filakovský, P. Franek, U. Wagner, S.Y. Zhechev, Journal of Applied and Computational Topology 2 (2018) 177–231.","mla":"Filakovský, Marek, et al. “Computing Simplicial Representatives of Homotopy Group Elements.” Journal of Applied and Computational Topology, vol. 2, no. 3–4, Springer, 2018, pp. 177–231, doi:10.1007/s41468-018-0021-5.","chicago":"Filakovský, Marek, Peter Franek, Uli Wagner, and Stephan Y Zhechev. “Computing Simplicial Representatives of Homotopy Group Elements.” Journal of Applied and Computational Topology. Springer, 2018. https://doi.org/10.1007/s41468-018-0021-5.","ama":"Filakovský M, Franek P, Wagner U, Zhechev SY. Computing simplicial representatives of homotopy group elements. Journal of Applied and Computational Topology. 2018;2(3-4):177-231. doi:10.1007/s41468-018-0021-5","ieee":"M. Filakovský, P. Franek, U. Wagner, and S. Y. Zhechev, “Computing simplicial representatives of homotopy group elements,” Journal of Applied and Computational Topology, vol. 2, no. 3–4. Springer, pp. 177–231, 2018.","apa":"Filakovský, M., Franek, P., Wagner, U., & Zhechev, S. Y. (2018). Computing simplicial representatives of homotopy group elements. Journal of Applied and Computational Topology. Springer. https://doi.org/10.1007/s41468-018-0021-5","ista":"Filakovský M, Franek P, Wagner U, Zhechev SY. 2018. Computing simplicial representatives of homotopy group elements. Journal of Applied and Computational Topology. 2(3–4), 177–231."}},{"article_processing_charge":"No","day":"18","scopus_import":"1","date_published":"2018-12-18T00:00:00Z","page":"229-241","citation":{"apa":"Fulek, R., & Tóth, C. D. (2018). Crossing minimization in perturbed drawings (Vol. 11282, pp. 229–241). Presented at the Graph Drawing and Network Visualization, Barcelona, Spain: Springer. https://doi.org/10.1007/978-3-030-04414-5_16","ieee":"R. Fulek and C. D. Tóth, “Crossing minimization in perturbed drawings,” presented at the Graph Drawing and Network Visualization, Barcelona, Spain, 2018, vol. 11282, pp. 229–241.","ista":"Fulek R, Tóth CD. 2018. Crossing minimization in perturbed drawings. Graph Drawing and Network Visualization, LNCS, vol. 11282, 229–241.","ama":"Fulek R, Tóth CD. Crossing minimization in perturbed drawings. In: Vol 11282. Springer; 2018:229-241. doi:10.1007/978-3-030-04414-5_16","chicago":"Fulek, Radoslav, and Csaba D. Tóth. “Crossing Minimization in Perturbed Drawings,” 11282:229–41. Springer, 2018. https://doi.org/10.1007/978-3-030-04414-5_16.","short":"R. Fulek, C.D. Tóth, in:, Springer, 2018, pp. 229–241.","mla":"Fulek, Radoslav, and Csaba D. Tóth. Crossing Minimization in Perturbed Drawings. Vol. 11282, Springer, 2018, pp. 229–41, doi:10.1007/978-3-030-04414-5_16."},"abstract":[{"lang":"eng","text":"Due to data compression or low resolution, nearby vertices and edges of a graph drawing may be bundled to a common node or arc. We model such a “compromised” drawing by a piecewise linear map φ:G → ℝ. We wish to perturb φ by an arbitrarily small ε>0 into a proper drawing (in which the vertices are distinct points, any two edges intersect in finitely many points, and no three edges have a common interior point) that minimizes the number of crossings. An ε-perturbation, for every ε>0, is given by a piecewise linear map (Formula Presented), where with ||·|| is the uniform norm (i.e., sup norm). We present a polynomial-time solution for this optimization problem when G is a cycle and the map φ has no spurs (i.e., no two adjacent edges are mapped to overlapping arcs). We also show that the problem becomes NP-complete (i) when G is an arbitrary graph and φ has no spurs, and (ii) when φ may have spurs and G is a cycle or a union of disjoint paths."}],"alternative_title":["LNCS"],"type":"conference","oa_version":"Preprint","title":"Crossing minimization in perturbed drawings","status":"public","_id":"5791","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"isbn":["9783030044138"]},"month":"12","language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-04414-5_16","conference":{"location":"Barcelona, Spain","start_date":"2018-09-26","end_date":"2018-09-28","name":"Graph Drawing and Network Visualization"},"isi":1,"quality_controlled":"1","external_id":{"arxiv":["1808.07608"],"isi":["000672802500016"]},"main_file_link":[{"url":"https://arxiv.org/abs/1808.07608","open_access":"1"}],"oa":1,"volume":"11282 ","date_created":"2018-12-30T22:59:15Z","date_updated":"2023-09-11T12:49:55Z","author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","first_name":"Radoslav","last_name":"Fulek","full_name":"Fulek, Radoslav"},{"full_name":"Tóth, Csaba D.","last_name":"Tóth","first_name":"Csaba D."}],"department":[{"_id":"UlWa"}],"publisher":"Springer","publication_status":"published","year":"2018"},{"article_number":"5","publist_id":"7398","ec_funded":1,"year":"2018","publisher":"ACM","department":[{"_id":"UlWa"}],"publication_status":"published","related_material":{"record":[{"id":"2157","relation":"earlier_version","status":"public"}]},"author":[{"full_name":"Matoušek, Jiří","first_name":"Jiří","last_name":"Matoušek"},{"full_name":"Sedgwick, Eric","first_name":"Eric","last_name":"Sedgwick"},{"full_name":"Tancer, Martin","id":"38AC689C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1191-6714","first_name":"Martin","last_name":"Tancer"},{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"}],"volume":65,"date_created":"2018-12-11T11:46:24Z","date_updated":"2023-09-11T13:38:49Z","month":"01","external_id":{"isi":["000425685900006"],"arxiv":["1402.0815"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1402.0815","open_access":"1"}],"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"isi":1,"quality_controlled":"1","doi":"10.1145/3078632","language":[{"iso":"eng"}],"type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in R3? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S3. The main step, which allows us to simplify X and recurse, is in proving that if X can be embedded in S3, then there is also an embedding in which X has a short meridian, that is, an essential curve in the boundary of X bounding a disk in S3 \\ X with length bounded by a computable function of the number of tetrahedra of X."}],"_id":"425","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":" 65","title":"Embeddability in the 3-Sphere is decidable","status":"public","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"chicago":"Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Embeddability in the 3-Sphere Is Decidable.” Journal of the ACM. ACM, 2018. https://doi.org/10.1145/3078632.","mla":"Matoušek, Jiří, et al. “Embeddability in the 3-Sphere Is Decidable.” Journal of the ACM, vol. 65, no. 1, 5, ACM, 2018, doi:10.1145/3078632.","short":"J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, Journal of the ACM 65 (2018).","ista":"Matoušek J, Sedgwick E, Tancer M, Wagner U. 2018. Embeddability in the 3-Sphere is decidable. Journal of the ACM. 65(1), 5.","ieee":"J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Embeddability in the 3-Sphere is decidable,” Journal of the ACM, vol. 65, no. 1. ACM, 2018.","apa":"Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2018). Embeddability in the 3-Sphere is decidable. Journal of the ACM. ACM. https://doi.org/10.1145/3078632","ama":"Matoušek J, Sedgwick E, Tancer M, Wagner U. Embeddability in the 3-Sphere is decidable. Journal of the ACM. 2018;65(1). doi:10.1145/3078632"},"publication":"Journal of the ACM","article_type":"original","date_published":"2018-01-01T00:00:00Z"},{"abstract":[{"lang":"eng","text":"We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding ' : G ! M of a graph G into a 2manifold M maps the vertices in V (G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to a common node or arc, due to data compression or low resolution. This raises the computational problem of deciding whether a given map ' : G ! M comes from an embedding. A map ' : G ! M is a weak embedding if it can be perturbed into an embedding ψ: G ! M with k' \"k < \" for every " > 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl [14], which reduces to solving a system of linear equations over Z2. It runs in O(n2!) O(n4:75) time, where 2:373 is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler than [14]: We perform a sequence of local operations that gradually "untangles" the image '(G) into an embedding (G), or reports that ' is not a weak embedding. It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon [1], and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations."}],"type":"conference","oa_version":"Preprint","_id":"309","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Recognizing weak embeddings of graphs","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2018-01-01T00:00:00Z","citation":{"chicago":"Akitaya, Hugo, Radoslav Fulek, and Csaba Tóth. “Recognizing Weak Embeddings of Graphs,” 274–92. ACM, 2018. https://doi.org/10.1137/1.9781611975031.20.","mla":"Akitaya, Hugo, et al. Recognizing Weak Embeddings of Graphs. ACM, 2018, pp. 274–92, doi:10.1137/1.9781611975031.20.","short":"H. Akitaya, R. Fulek, C. Tóth, in:, ACM, 2018, pp. 274–292.","ista":"Akitaya H, Fulek R, Tóth C. 2018. Recognizing weak embeddings of graphs. SODA: Symposium on Discrete Algorithms, 274–292.","ieee":"H. Akitaya, R. Fulek, and C. Tóth, “Recognizing weak embeddings of graphs,” presented at the SODA: Symposium on Discrete Algorithms, New Orleans, LA, USA, 2018, pp. 274–292.","apa":"Akitaya, H., Fulek, R., & Tóth, C. (2018). Recognizing weak embeddings of graphs (pp. 274–292). Presented at the SODA: Symposium on Discrete Algorithms, New Orleans, LA, USA: ACM. https://doi.org/10.1137/1.9781611975031.20","ama":"Akitaya H, Fulek R, Tóth C. Recognizing weak embeddings of graphs. In: ACM; 2018:274-292. doi:10.1137/1.9781611975031.20"},"page":"274 - 292","publist_id":"7556","related_material":{"record":[{"id":"6982","relation":"later_version","status":"public"}]},"author":[{"first_name":"Hugo","last_name":"Akitaya","full_name":"Akitaya, Hugo"},{"first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav"},{"full_name":"Tóth, Csaba","first_name":"Csaba","last_name":"Tóth"}],"date_created":"2018-12-11T11:45:45Z","date_updated":"2023-09-15T12:19:32Z","acknowledgement":"∗Research supported in part by the NSF awards CCF-1422311 and CCF-1423615, and the Science Without Borders program. The second author gratefully acknowledges support from Austrian Science Fund (FWF): M2281-N35.","year":"2018","department":[{"_id":"UlWa"}],"publisher":"ACM","publication_status":"published","month":"01","doi":"10.1137/1.9781611975031.20","conference":{"name":"SODA: Symposium on Discrete Algorithms","end_date":"2018-01-10","start_date":"2018-01-07","location":"New Orleans, LA, USA"},"language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1709.09209","open_access":"1"}],"external_id":{"isi":["000483921200021"],"arxiv":["1709.09209"]},"project":[{"name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF","_id":"261FA626-B435-11E9-9278-68D0E5697425","grant_number":"M02281"}],"isi":1,"quality_controlled":"1"},{"page":"1500-1516","citation":{"apa":"Rohou, S., Franek, P., Aubry, C., & Jaulin, L. (2018). Proving the existence of loops in robot trajectories. The International Journal of Robotics Research. SAGE Publications. https://doi.org/10.1177/0278364918808367","ieee":"S. Rohou, P. Franek, C. Aubry, and L. Jaulin, “Proving the existence of loops in robot trajectories,” The International Journal of Robotics Research, vol. 37, no. 12. SAGE Publications, pp. 1500–1516, 2018.","ista":"Rohou S, Franek P, Aubry C, Jaulin L. 2018. Proving the existence of loops in robot trajectories. The International Journal of Robotics Research. 37(12), 1500–1516.","ama":"Rohou S, Franek P, Aubry C, Jaulin L. Proving the existence of loops in robot trajectories. The International Journal of Robotics Research. 2018;37(12):1500-1516. doi:10.1177/0278364918808367","chicago":"Rohou, Simon, Peter Franek, Clément Aubry, and Luc Jaulin. “Proving the Existence of Loops in Robot Trajectories.” The International Journal of Robotics Research. SAGE Publications, 2018. https://doi.org/10.1177/0278364918808367.","short":"S. Rohou, P. Franek, C. Aubry, L. Jaulin, The International Journal of Robotics Research 37 (2018) 1500–1516.","mla":"Rohou, Simon, et al. “Proving the Existence of Loops in Robot Trajectories.” The International Journal of Robotics Research, vol. 37, no. 12, SAGE Publications, 2018, pp. 1500–16, doi:10.1177/0278364918808367."},"publication":"The International Journal of Robotics Research","date_published":"2018-10-24T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"24","intvolume":" 37","status":"public","title":"Proving the existence of loops in robot trajectories","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"5960","oa_version":"Preprint","type":"journal_article","issue":"12","abstract":[{"text":"In this paper we present a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points in simultaneous localization and mapping (SLAM) methods, especially in homogeneous environments with difficult scenes recognitions. The proposed approach is generic and could be coupled with conventional SLAM algorithms to reliably reduce their computing burden, thus improving the localization and mapping processes in the most challenging environments such as unexplored underwater extents. To prove that a robot performed a loop whatever the uncertainties in its evolution, we employ the notion of topological degree that originates in the field of differential topology. We show that a verification tool based on the topological degree is an optimal method for proving robot loops. This is demonstrated both on datasets from real missions involving autonomous underwater vehicles and by a mathematical discussion.","lang":"eng"}],"isi":1,"quality_controlled":"1","oa":1,"external_id":{"arxiv":["1712.01341"],"isi":["000456881100004"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1712.01341"}],"language":[{"iso":"eng"}],"doi":"10.1177/0278364918808367","publication_identifier":{"issn":["0278-3649"],"eissn":["1741-3176"]},"month":"10","department":[{"_id":"UlWa"}],"publisher":"SAGE Publications","publication_status":"published","year":"2018","volume":37,"date_updated":"2023-09-19T10:41:59Z","date_created":"2019-02-13T09:36:20Z","author":[{"last_name":"Rohou","first_name":"Simon","full_name":"Rohou, Simon"},{"full_name":"Franek, Peter","orcid":"0000-0001-8878-8397","id":"473294AE-F248-11E8-B48F-1D18A9856A87","last_name":"Franek","first_name":"Peter"},{"last_name":"Aubry","first_name":"Clément","full_name":"Aubry, Clément"},{"full_name":"Jaulin, Luc","first_name":"Luc","last_name":"Jaulin"}]},{"type":"journal_article","abstract":[{"text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle.","lang":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"6355","intvolume":" 6","status":"public","title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","ddc":["510"],"file":[{"creator":"dernst","file_size":249246,"content_type":"application/pdf","file_name":"2018_ForumMahtematics_Akopyan.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:28Z","date_created":"2019-04-30T06:14:58Z","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","file_id":"6356","relation":"main_file"}],"oa_version":"Published Version","has_accepted_license":"1","article_processing_charge":"No","day":"31","citation":{"ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7."},"publication":"Forum of Mathematics, Sigma","date_published":"2018-05-31T00:00:00Z","article_number":"e7","ec_funded":1,"file_date_updated":"2020-07-14T12:47:28Z","year":"2018","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"Cambridge University Press","publication_status":"published","related_material":{"record":[{"id":"8156","status":"public","relation":"dissertation_contains"}]},"author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","first_name":"Sergey"}],"volume":6,"date_created":"2019-04-30T06:09:57Z","date_updated":"2023-09-19T14:50:12Z","publication_identifier":{"issn":["2050-5094"]},"month":"05","external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"quality_controlled":"1","isi":1,"doi":"10.1017/fms.2018.7","language":[{"iso":"eng"}]},{"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"1378"}]},"author":[{"full_name":"Dotterrer, Dominic","first_name":"Dominic","last_name":"Dotterrer"},{"full_name":"Kaufman, Tali","first_name":"Tali","last_name":"Kaufman"},{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"}],"volume":195,"date_created":"2018-12-11T11:48:16Z","date_updated":"2023-09-27T12:29:57Z","year":"2018","publisher":"Springer","department":[{"_id":"UlWa"}],"publication_status":"published","publist_id":"6925","file_date_updated":"2020-07-14T12:47:58Z","doi":"10.1007/s10711-017-0291-4","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000437122700017"]},"oa":1,"project":[{"name":"Embeddings in Higher Dimensions: Algorithms and Combinatorics","grant_number":"PP00P2_138948","_id":"25FA3206-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","month":"08","pubrep_id":"912","oa_version":"Published Version","file":[{"file_name":"s10711-017-0291-4.pdf","access_level":"open_access","file_size":412486,"content_type":"application/pdf","creator":"kschuh","relation":"main_file","file_id":"5835","date_updated":"2020-07-14T12:47:58Z","date_created":"2019-01-15T13:44:05Z","checksum":"d2f70fc132156504aa4c626aa378a7ab"}],"_id":"742","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":" 195","title":"On expansion and topological overlap","ddc":["514","516"],"status":"public","issue":"1","abstract":[{"text":"We give a detailed and easily accessible proof of Gromov’s Topological Overlap Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension d. Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are defined in terms of cellular cochains of X) then X has the following topological overlap property: for every continuous map (Formula presented.) there exists a point (Formula presented.) that is contained in the images of a positive fraction (Formula presented.) of the d-cells of X. More generally, the conclusion holds if (Formula presented.) is replaced by any d-dimensional piecewise-linear manifold M, with a constant (Formula presented.) that depends only on d and on the expansion properties of X, but not on M.","lang":"eng"}],"type":"journal_article","date_published":"2018-08-01T00:00:00Z","citation":{"chicago":"Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological Overlap.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0291-4.","short":"D. Dotterrer, T. Kaufman, U. Wagner, Geometriae Dedicata 195 (2018) 307–317.","mla":"Dotterrer, Dominic, et al. “On Expansion and Topological Overlap.” Geometriae Dedicata, vol. 195, no. 1, Springer, 2018, pp. 307–317, doi:10.1007/s10711-017-0291-4.","ieee":"D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,” Geometriae Dedicata, vol. 195, no. 1. Springer, pp. 307–317, 2018.","apa":"Dotterrer, D., Kaufman, T., & Wagner, U. (2018). On expansion and topological overlap. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0291-4","ista":"Dotterrer D, Kaufman T, Wagner U. 2018. On expansion and topological overlap. Geometriae Dedicata. 195(1), 307–317.","ama":"Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. Geometriae Dedicata. 2018;195(1):307–317. doi:10.1007/s10711-017-0291-4"},"publication":"Geometriae Dedicata","page":"307–317","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1"},{"language":[{"iso":"eng"}],"doi":"10.7155/jgaa.00408","quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["1608.08662"]},"oa":1,"month":"01","date_created":"2018-12-11T11:50:13Z","date_updated":"2023-02-23T10:05:57Z","volume":21,"author":[{"last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","full_name":"Fulek, Radoslav"},{"first_name":"Michael","last_name":"Pelsmajer","full_name":"Pelsmajer, Michael"},{"full_name":"Schaefer, Marcus","first_name":"Marcus","last_name":"Schaefer"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"1164"},{"id":"1595","relation":"earlier_version","status":"public"}]},"publication_status":"published","publisher":"Brown University","department":[{"_id":"UlWa"}],"year":"2017","file_date_updated":"2019-10-24T10:54:37Z","ec_funded":1,"publist_id":"6254","date_published":"2017-01-01T00:00:00Z","article_type":"original","page":"135 - 154","publication":"Journal of Graph Algorithms and Applications","citation":{"mla":"Fulek, Radoslav, et al. “Hanani-Tutte for Radial Planarity.” Journal of Graph Algorithms and Applications, vol. 21, no. 1, Brown University, 2017, pp. 135–54, doi:10.7155/jgaa.00408.","short":"R. Fulek, M. Pelsmajer, M. Schaefer, Journal of Graph Algorithms and Applications 21 (2017) 135–154.","chicago":"Fulek, Radoslav, Michael Pelsmajer, and Marcus Schaefer. “Hanani-Tutte for Radial Planarity.” Journal of Graph Algorithms and Applications. Brown University, 2017. https://doi.org/10.7155/jgaa.00408.","ama":"Fulek R, Pelsmajer M, Schaefer M. Hanani-Tutte for radial planarity. Journal of Graph Algorithms and Applications. 2017;21(1):135-154. doi:10.7155/jgaa.00408","ista":"Fulek R, Pelsmajer M, Schaefer M. 2017. Hanani-Tutte for radial planarity. Journal of Graph Algorithms and Applications. 21(1), 135–154.","apa":"Fulek, R., Pelsmajer, M., & Schaefer, M. (2017). Hanani-Tutte for radial planarity. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00408","ieee":"R. Fulek, M. Pelsmajer, and M. Schaefer, “Hanani-Tutte for radial planarity,” Journal of Graph Algorithms and Applications, vol. 21, no. 1. Brown University, pp. 135–154, 2017."},"day":"01","article_processing_charge":"No","has_accepted_license":"1","scopus_import":1,"file":[{"date_updated":"2019-10-24T10:54:37Z","date_created":"2019-10-24T10:54:37Z","success":1,"relation":"main_file","file_id":"6967","file_size":573623,"content_type":"application/pdf","creator":"dernst","file_name":"2017_JournalGraphAlgorithms_Fulek.pdf","access_level":"open_access"}],"oa_version":"Published Version","ddc":["510"],"title":"Hanani-Tutte for radial planarity","status":"public","intvolume":" 21","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1113","abstract":[{"lang":"eng","text":"A drawing of a graph G is radial if the vertices of G are placed on concentric circles C 1 , . . . , C k with common center c , and edges are drawn radially : every edge intersects every circle centered at c at most once. G is radial planar if it has a radial embedding, that is, a crossing-free radial drawing. If the vertices of G are ordered or partitioned into ordered levels (as they are for leveled graphs), we require that the assignment of vertices to circles corresponds to the given ordering or leveling. We show that a graph G is radial planar if G has a radial drawing in which every two edges cross an even number of times; the radial embedding has the same leveling as the radial drawing. In other words, we establish the weak variant of the Hanani-Tutte theorem for radial planarity. This generalizes a result by Pach and Toth."}],"issue":"1","type":"journal_article"},{"abstract":[{"lang":"eng","text":"We investigate the complexity of finding an embedded non-orientable surface of Euler genus g in a triangulated 3-manifold. This problem occurs both as a natural question in low-dimensional topology, and as a first non-trivial instance of embeddability of complexes into 3-manifolds. We prove that the problem is NP-hard, thus adding to the relatively few hardness results that are currently known in 3-manifold topology. In addition, we show that the problem lies in NP when the Euler genus g is odd, and we give an explicit algorithm in this case."}],"issue":"4","type":"journal_article","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"534","status":"public","title":"Finding non-orientable surfaces in 3-Manifolds","intvolume":" 58","day":"09","article_processing_charge":"No","scopus_import":1,"date_published":"2017-06-09T00:00:00Z","publication":"Discrete & Computational Geometry","citation":{"chicago":"Burton, Benjamin, Arnaud N de Mesmay, and Uli Wagner. “Finding Non-Orientable Surfaces in 3-Manifolds.” Discrete & Computational Geometry. Springer, 2017. https://doi.org/10.1007/s00454-017-9900-0.","mla":"Burton, Benjamin, et al. “Finding Non-Orientable Surfaces in 3-Manifolds.” Discrete & Computational Geometry, vol. 58, no. 4, Springer, 2017, pp. 871–88, doi:10.1007/s00454-017-9900-0.","short":"B. Burton, A.N. de Mesmay, U. Wagner, Discrete & Computational Geometry 58 (2017) 871–888.","ista":"Burton B, de Mesmay AN, Wagner U. 2017. Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. 58(4), 871–888.","apa":"Burton, B., de Mesmay, A. N., & Wagner, U. (2017). Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9900-0","ieee":"B. Burton, A. N. de Mesmay, and U. Wagner, “Finding non-orientable surfaces in 3-Manifolds,” Discrete & Computational Geometry, vol. 58, no. 4. Springer, pp. 871–888, 2017.","ama":"Burton B, de Mesmay AN, Wagner U. Finding non-orientable surfaces in 3-Manifolds. Discrete & Computational Geometry. 2017;58(4):871-888. doi:10.1007/s00454-017-9900-0"},"article_type":"original","page":"871 - 888","publist_id":"7283","author":[{"last_name":"Burton","first_name":"Benjamin","full_name":"Burton, Benjamin"},{"first_name":"Arnaud N","last_name":"De Mesmay","id":"3DB2F25C-F248-11E8-B48F-1D18A9856A87","full_name":"De Mesmay, Arnaud N"},{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"1379"}]},"date_created":"2018-12-11T11:47:01Z","date_updated":"2023-02-21T17:01:34Z","volume":58,"year":"2017","publication_status":"published","publisher":"Springer","department":[{"_id":"UlWa"}],"month":"06","publication_identifier":{"issn":["01795376"]},"doi":"10.1007/s00454-017-9900-0","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.07907"}],"oa":1,"external_id":{"arxiv":["1602.07907"]},"quality_controlled":"1"},{"author":[{"full_name":"Franek, Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Franek"},{"full_name":"Krcál, Marek","first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"volume":19,"date_updated":"2021-01-12T08:03:12Z","date_created":"2018-12-11T11:47:14Z","year":"2017","publisher":"International Press","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication_status":"published","publist_id":"7246","ec_funded":1,"doi":"10.4310/HHA.2017.v19.n2.a16","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.04310"}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"},{"_id":"2590DB08-B435-11E9-9278-68D0E5697425","grant_number":"701309","name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","call_identifier":"H2020"}],"quality_controlled":"1","publication_identifier":{"issn":["15320073"]},"month":"01","oa_version":"Submitted Version","_id":"568","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","intvolume":" 19","title":"Persistence of zero sets","status":"public","issue":"2","abstract":[{"text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).","lang":"eng"}],"type":"journal_article","date_published":"2017-01-01T00:00:00Z","citation":{"chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.","short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16","ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16"},"publication":"Homology, Homotopy and Applications","page":"313 - 342","day":"01","scopus_import":1},{"abstract":[{"lang":"eng","text":"The fact that the complete graph K5 does not embed in the plane has been generalized in two independent directions. On the one hand, the solution of the classical Heawood problem for graphs on surfaces established that the complete graph Kn embeds in a closed surface M (other than the Klein bottle) if and only if (n−3)(n−4) ≤ 6b1(M), where b1(M) is the first Z2-Betti number of M. On the other hand, van Kampen and Flores proved that the k-skeleton of the n-dimensional simplex (the higher-dimensional analogue of Kn+1) embeds in R2k if and only if n ≤ 2k + 1. Two decades ago, Kühnel conjectured that the k-skeleton of the n-simplex embeds in a compact, (k − 1)-connected 2k-manifold with kth Z2-Betti number bk only if the following generalized Heawood inequality holds: (k+1 n−k−1) ≤ (k+1 2k+1)bk. This is a common generalization of the case of graphs on surfaces as well as the van Kampen–Flores theorem. In the spirit of Kühnel’s conjecture, we prove that if the k-skeleton of the n-simplex embeds in a compact 2k-manifold with kth Z2-Betti number bk, then n ≤ 2bk(k 2k+2)+2k+4. This bound is weaker than the generalized Heawood inequality, but does not require the assumption that M is (k−1)-connected. Our results generalize to maps without q-covered points, in the spirit of Tverberg’s theorem, for q a prime power. Our proof uses a result of Volovikov about maps that satisfy a certain homological triviality condition."}],"issue":"2","type":"journal_article","oa_version":"Preprint","status":"public","title":"On generalized Heawood inequalities for manifolds: A van Kampen–Flores type nonembeddability result","intvolume":" 222","_id":"610","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","scopus_import":1,"date_published":"2017-10-01T00:00:00Z","page":"841 - 866","publication":"Israel Journal of Mathematics","citation":{"ama":"Goaoc X, Mabillard I, Paták P, Patakova Z, Tancer M, Wagner U. On generalized Heawood inequalities for manifolds: A van Kampen–Flores type nonembeddability result. Israel Journal of Mathematics. 2017;222(2):841-866. doi:10.1007/s11856-017-1607-7","ista":"Goaoc X, Mabillard I, Paták P, Patakova Z, Tancer M, Wagner U. 2017. On generalized Heawood inequalities for manifolds: A van Kampen–Flores type nonembeddability result. Israel Journal of Mathematics. 222(2), 841–866.","ieee":"X. Goaoc, I. Mabillard, P. Paták, Z. Patakova, M. Tancer, and U. Wagner, “On generalized Heawood inequalities for manifolds: A van Kampen–Flores type nonembeddability result,” Israel Journal of Mathematics, vol. 222, no. 2. Springer, pp. 841–866, 2017.","apa":"Goaoc, X., Mabillard, I., Paták, P., Patakova, Z., Tancer, M., & Wagner, U. (2017). On generalized Heawood inequalities for manifolds: A van Kampen–Flores type nonembeddability result. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-017-1607-7","mla":"Goaoc, Xavier, et al. “On Generalized Heawood Inequalities for Manifolds: A van Kampen–Flores Type Nonembeddability Result.” Israel Journal of Mathematics, vol. 222, no. 2, Springer, 2017, pp. 841–66, doi:10.1007/s11856-017-1607-7.","short":"X. Goaoc, I. Mabillard, P. Paták, Z. Patakova, M. Tancer, U. Wagner, Israel Journal of Mathematics 222 (2017) 841–866.","chicago":"Goaoc, Xavier, Isaac Mabillard, Pavel Paták, Zuzana Patakova, Martin Tancer, and Uli Wagner. “On Generalized Heawood Inequalities for Manifolds: A van Kampen–Flores Type Nonembeddability Result.” Israel Journal of Mathematics. Springer, 2017. https://doi.org/10.1007/s11856-017-1607-7."},"ec_funded":1,"publist_id":"7194","date_updated":"2023-02-23T10:02:13Z","date_created":"2018-12-11T11:47:29Z","volume":222,"author":[{"first_name":"Xavier","last_name":"Goaoc","full_name":"Goaoc, Xavier"},{"full_name":"Mabillard, Isaac","id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","first_name":"Isaac","last_name":"Mabillard"},{"full_name":"Paták, Pavel","last_name":"Paták","first_name":"Pavel"},{"first_name":"Zuzana","last_name":"Patakova","id":"48B57058-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3975-1683","full_name":"Patakova, Zuzana"},{"full_name":"Tancer, Martin","id":"38AC689C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1191-6714","first_name":"Martin","last_name":"Tancer"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli"}],"related_material":{"record":[{"id":"1511","status":"public","relation":"earlier_version"}]},"publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer","acknowledgement":"The work by Z. P. was partially supported by the Israel Science Foundation grant ISF-768/12. The work by Z. P. and M. T. was partially supported by the project CE-ITI (GACR P202/12/G061) of the Czech Science Foundation and by the ERC Advanced Grant No. 267165. Part of the research work of M.T. was conducted at IST Austria, supported by an IST Fellowship. The research of P. P. was supported by the ERC Advanced grant no. 320924. The work by I. M. and U. W. was supported by the Swiss National Science Foundation (grants SNSF-200020-138230 and SNSF-PP00P2-138948). The collaboration between U. W. and X. G. was partially supported by the LabEx Bézout (ANR-10-LABX-58).","year":"2017","month":"10","language":[{"iso":"eng"}],"doi":"10.1007/s11856-017-1607-7","quality_controlled":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"main_file_link":[{"url":"https://arxiv.org/abs/1610.09063","open_access":"1"}],"oa":1},{"volume":92,"date_created":"2019-06-04T12:11:52Z","date_updated":"2021-01-12T08:07:51Z","author":[{"first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2017","ec_funded":1,"file_date_updated":"2020-07-14T12:47:33Z","article_number":"34","language":[{"iso":"eng"}],"doi":"10.4230/LIPICS.ISAAC.2017.34","conference":{"name":"ISAAC: International Symposium on Algorithms and Computation","location":"Phuket, Thailand","start_date":"2017-12-09","end_date":"2017-12-22"},"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs","grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"month":"12","file":[{"date_updated":"2020-07-14T12:47:33Z","date_created":"2019-06-04T12:20:35Z","checksum":"fc7a643e29621c8bbe49d36b39081f31","file_id":"6518","relation":"main_file","creator":"kschuh","file_size":588982,"content_type":"application/pdf","file_name":"2017_LIPIcs-Fulek.pdf","access_level":"open_access"}],"oa_version":"Published Version","intvolume":" 92","title":"Embedding graphs into embedded graphs","ddc":["510"],"status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6517","abstract":[{"text":"A (possibly degenerate) drawing of a graph G in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a drawing of a planar graph G in the plane is approximable by an embedding, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class, i.e., the rotation system (or equivalently the faces) of the embedding of G and the choice of outer face are fixed. In other words, we show that c-planarity with embedded pipes is tractable for graphs with fixed embeddings. To the best of our knowledge an analogous result was previously known essentially only when G is a cycle.","lang":"eng"}],"type":"conference","date_published":"2017-12-01T00:00:00Z","citation":{"apa":"Fulek, R. (2017). Embedding graphs into embedded graphs (Vol. 92). Presented at the ISAAC: International Symposium on Algorithms and Computation, Phuket, Thailand: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ISAAC.2017.34","ieee":"R. Fulek, “Embedding graphs into embedded graphs,” presented at the ISAAC: International Symposium on Algorithms and Computation, Phuket, Thailand, 2017, vol. 92.","ista":"Fulek R. 2017. Embedding graphs into embedded graphs. ISAAC: International Symposium on Algorithms and Computation vol. 92, 34.","ama":"Fulek R. Embedding graphs into embedded graphs. In: Vol 92. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:10.4230/LIPICS.ISAAC.2017.34","chicago":"Fulek, Radoslav. “Embedding Graphs into Embedded Graphs,” Vol. 92. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPICS.ISAAC.2017.34.","short":"R. Fulek, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.","mla":"Fulek, Radoslav. Embedding Graphs into Embedded Graphs. Vol. 92, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:10.4230/LIPICS.ISAAC.2017.34."},"has_accepted_license":"1","day":"01","scopus_import":1},{"type":"conference","alternative_title":["LIPIcs"],"abstract":[{"text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. ","lang":"eng"}],"_id":"688","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 77","title":"Topological data analysis with Bregman divergences","ddc":["514","516"],"status":"public","pubrep_id":"895","oa_version":"Published Version","file":[{"date_updated":"2020-07-14T12:47:42Z","date_created":"2018-12-12T10:11:03Z","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","relation":"main_file","file_id":"4856","content_type":"application/pdf","file_size":990546,"creator":"system","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","access_level":"open_access"}],"scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","apa":"Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","mla":"Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.","short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39."},"page":"391-3916","date_published":"2017-06-01T00:00:00Z","publist_id":"7021","file_date_updated":"2020-07-14T12:47:42Z","year":"2017","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publication_status":"published","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"volume":77,"date_created":"2018-12-11T11:47:56Z","date_updated":"2021-01-12T08:09:26Z","publication_identifier":{"issn":["18688969"]},"month":"06","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2017.39","conference":{"name":"Symposium on Computational Geometry, SoCG","location":"Brisbane, Australia","start_date":"2017-07-04","end_date":"2017-07-07"},"language":[{"iso":"eng"}]},{"publist_id":"6996","file_date_updated":"2020-07-14T12:47:47Z","year":"2017","department":[{"_id":"UlWa"}],"publisher":"International Press","publication_status":"published","author":[{"full_name":"Kynčl, Jan","last_name":"Kynčl","first_name":"Jan"},{"orcid":"0000-0002-3975-1683","id":"48B57058-F248-11E8-B48F-1D18A9856A87","last_name":"Patakova","first_name":"Zuzana","full_name":"Patakova, Zuzana"}],"volume":24,"date_created":"2018-12-11T11:48:00Z","date_updated":"2021-01-12T08:11:28Z","publication_identifier":{"issn":["10778926"]},"month":"07","oa":1,"quality_controlled":"1","language":[{"iso":"eng"}],"type":"journal_article","issue":"3","abstract":[{"lang":"eng","text":"A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2+b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d ≥ 3, have k = m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m^3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m^2."}],"_id":"701","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 24","ddc":["500"],"title":"On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4","status":"public","pubrep_id":"984","oa_version":"Submitted Version","file":[{"file_name":"IST-2018-984-v1+1_Patakova_on_the_nonexistence_of_k-reptile_simplices_in_R_3_and_R_4_2017.pdf","access_level":"open_access","creator":"system","content_type":"application/pdf","file_size":544042,"file_id":"5077","relation":"main_file","date_created":"2018-12-12T10:14:25Z","date_updated":"2020-07-14T12:47:47Z","checksum":"a431e573e31df13bc0f66de3061006ec"}],"has_accepted_license":"1","day":"14","citation":{"ama":"Kynčl J, Patakova Z. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. 2017;24(3):1-44.","ista":"Kynčl J, Patakova Z. 2017. On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. 24(3), 1–44.","ieee":"J. Kynčl and Z. Patakova, “On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4,” The Electronic Journal of Combinatorics, vol. 24, no. 3. International Press, pp. 1–44, 2017.","apa":"Kynčl, J., & Patakova, Z. (2017). On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4. The Electronic Journal of Combinatorics. International Press.","mla":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” The Electronic Journal of Combinatorics, vol. 24, no. 3, International Press, 2017, pp. 1–44.","short":"J. Kynčl, Z. Patakova, The Electronic Journal of Combinatorics 24 (2017) 1–44.","chicago":"Kynčl, Jan, and Zuzana Patakova. “On the Nonexistence of k Reptile Simplices in ℝ^3 and ℝ^4.” The Electronic Journal of Combinatorics. International Press, 2017."},"publication":"The Electronic Journal of Combinatorics","page":"1-44","date_published":"2017-07-14T00:00:00Z"},{"publication_identifier":{"issn":["10778926"]},"month":"07","doi":"10.37236/6663","language":[{"iso":"eng"}],"oa":1,"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","ec_funded":1,"publist_id":"6859","file_date_updated":"2020-07-14T12:48:06Z","article_number":"P3.18","author":[{"orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek","first_name":"Radoslav","full_name":"Fulek, Radoslav"},{"first_name":"Jan","last_name":"Kynčl","full_name":"Kynčl, Jan"},{"full_name":"Pálvölgyi, Dömötör","last_name":"Pálvölgyi","first_name":"Dömötör"}],"volume":24,"date_created":"2018-12-11T11:48:32Z","date_updated":"2022-03-18T12:58:53Z","year":"2017","department":[{"_id":"UlWa"}],"publisher":"International Press","publication_status":"published","has_accepted_license":"1","article_processing_charge":"No","day":"28","scopus_import":"1","date_published":"2017-07-28T00:00:00Z","citation":{"chicago":"Fulek, Radoslav, Jan Kynčl, and Dömötör Pálvölgyi. “Unified Hanani Tutte Theorem.” Electronic Journal of Combinatorics. International Press, 2017. https://doi.org/10.37236/6663.","mla":"Fulek, Radoslav, et al. “Unified Hanani Tutte Theorem.” Electronic Journal of Combinatorics, vol. 24, no. 3, P3.18, International Press, 2017, doi:10.37236/6663.","short":"R. Fulek, J. Kynčl, D. Pálvölgyi, Electronic Journal of Combinatorics 24 (2017).","ista":"Fulek R, Kynčl J, Pálvölgyi D. 2017. Unified Hanani Tutte theorem. Electronic Journal of Combinatorics. 24(3), P3.18.","ieee":"R. Fulek, J. Kynčl, and D. Pálvölgyi, “Unified Hanani Tutte theorem,” Electronic Journal of Combinatorics, vol. 24, no. 3. International Press, 2017.","apa":"Fulek, R., Kynčl, J., & Pálvölgyi, D. (2017). Unified Hanani Tutte theorem. Electronic Journal of Combinatorics. International Press. https://doi.org/10.37236/6663","ama":"Fulek R, Kynčl J, Pálvölgyi D. Unified Hanani Tutte theorem. Electronic Journal of Combinatorics. 2017;24(3). doi:10.37236/6663"},"publication":"Electronic Journal of Combinatorics","article_type":"original","issue":"3","abstract":[{"text":"We introduce a common generalization of the strong Hanani–Tutte theorem and the weak Hanani–Tutte theorem: if a graph G has a drawing D in the plane where every pair of independent edges crosses an even number of times, then G has a planar drawing preserving the rotation of each vertex whose incident edges cross each other evenly in D. The theorem is implicit in the proof of the strong Hanani–Tutte theorem by Pelsmajer, Schaefer and Štefankovič. We give a new, somewhat simpler proof.","lang":"eng"}],"type":"journal_article","file":[{"date_updated":"2020-07-14T12:48:06Z","date_created":"2019-01-18T14:04:08Z","checksum":"ef320cff0f062051e858f929be6a3581","file_id":"5853","relation":"main_file","creator":"dernst","file_size":236944,"content_type":"application/pdf","file_name":"2017_ElectrCombi_Fulek.pdf","access_level":"open_access"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"795","intvolume":" 24","ddc":["000"],"title":"Unified Hanani Tutte theorem","status":"public"},{"year":"2017","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"publication_status":"published","related_material":{"record":[{"id":"5986","status":"public","relation":"later_version"}]},"author":[{"full_name":"Lubiw, Anna","first_name":"Anna","last_name":"Lubiw"},{"last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli"}],"volume":77,"date_created":"2018-12-11T11:47:54Z","date_updated":"2023-09-05T15:01:43Z","article_number":"49","publist_id":"7033","file_date_updated":"2020-07-14T12:47:41Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2017.49","conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Brisbane, Australia","start_date":"2017-07-04","end_date":"2017-07-07"},"language":[{"iso":"eng"}],"month":"06","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"683","intvolume":" 77","title":"A proof of the orbit conjecture for flipping edge labelled triangulations","ddc":["514","516"],"status":"public","pubrep_id":"896","file":[{"file_name":"IST-2017-896-v1+1_LIPIcs-SoCG-2017-49.pdf","access_level":"open_access","content_type":"application/pdf","file_size":710007,"creator":"system","relation":"main_file","file_id":"5265","date_created":"2018-12-12T10:17:12Z","date_updated":"2020-07-14T12:47:41Z","checksum":"24fdde981cc513352a78dcf9b0660ae9"}],"oa_version":"Published Version","type":"conference","alternative_title":["LIPIcs"],"abstract":[{"lang":"eng","text":"Given a triangulation of a point set in the plane, a flip deletes an edge e whose removal leaves a convex quadrilateral, and replaces e by the opposite diagonal of the quadrilateral. It is well known that any triangulation of a point set can be reconfigured to any other triangulation by some sequence of flips. We explore this question in the setting where each edge of a triangulation has a label, and a flip transfers the label of the removed edge to the new edge. It is not true that every labelled triangulation of a point set can be reconfigured to every other labelled triangulation via a sequence of flips, but we characterize when this is possible. There is an obvious necessary condition: for each label l, if edge e has label l in the first triangulation and edge f has label l in the second triangulation, then there must be some sequence of flips that moves label l from e to f, ignoring all other labels. Bose, Lubiw, Pathak and Verdonschot formulated the Orbit Conjecture, which states that this necessary condition is also sufficient, i.e. that all labels can be simultaneously mapped to their destination if and only if each label individually can be mapped to its destination. We prove this conjecture. Furthermore, we give a polynomial-time algorithm to find a sequence of flips to reconfigure one labelled triangulation to another, if such a sequence exists, and we prove an upper bound of O(n7) on the length of the flip sequence. Our proof uses the topological result that the sets of pairwise non-crossing edges on a planar point set form a simplicial complex that is homeomorphic to a high-dimensional ball (this follows from a result of Orden and Santos; we give a different proof based on a shelling argument). The dual cell complex of this simplicial ball, called the flip complex, has the usual flip graph as its 1-skeleton. We use properties of the 2-skeleton of the flip complex to prove the Orbit Conjecture."}],"citation":{"apa":"Lubiw, A., Masárová, Z., & Wagner, U. (2017). A proof of the orbit conjecture for flipping edge labelled triangulations (Vol. 77). Presented at the SoCG: Symposium on Computational Geometry, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.49","ieee":"A. Lubiw, Z. Masárová, and U. Wagner, “A proof of the orbit conjecture for flipping edge labelled triangulations,” presented at the SoCG: Symposium on Computational Geometry, Brisbane, Australia, 2017, vol. 77.","ista":"Lubiw A, Masárová Z, Wagner U. 2017. A proof of the orbit conjecture for flipping edge labelled triangulations. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 77, 49.","ama":"Lubiw A, Masárová Z, Wagner U. A proof of the orbit conjecture for flipping edge labelled triangulations. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:10.4230/LIPIcs.SoCG.2017.49","chicago":"Lubiw, Anna, Zuzana Masárová, and Uli Wagner. “A Proof of the Orbit Conjecture for Flipping Edge Labelled Triangulations,” Vol. 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.49.","short":"A. Lubiw, Z. Masárová, U. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.","mla":"Lubiw, Anna, et al. A Proof of the Orbit Conjecture for Flipping Edge Labelled Triangulations. Vol. 77, 49, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:10.4230/LIPIcs.SoCG.2017.49."},"date_published":"2017-06-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01"},{"publist_id":"6309","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer","year":"2017","date_updated":"2023-09-20T12:01:28Z","date_created":"2018-12-11T11:50:00Z","volume":54,"author":[{"last_name":"Čadek","first_name":"Martin","full_name":"Čadek, Martin"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek"},{"full_name":"Vokřínek, Lukáš","first_name":"Lukáš","last_name":"Vokřínek"}],"month":"06","publication_identifier":{"issn":["01795376"]},"isi":1,"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1307.6444"}],"external_id":{"isi":["000400072700008"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00454-016-9855-6","type":"journal_article","abstract":[{"lang":"eng","text":"Let X and Y be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group G. Assuming that Y is d-connected and dimX≤2d, for some d≥1, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps |X|→|Y|; the existence of such a map can be decided even for dimX≤2d+1. This yields the first algorithm for deciding topological embeddability of a k-dimensional finite simplicial complex into Rn under the condition k≤23n−1. More generally, we present an algorithm that, given a lifting-extension problem satisfying an appropriate stability assumption, computes the set of all homotopy classes of solutions. This result is new even in the non-equivariant situation."}],"issue":"4","status":"public","title":"Algorithmic solvability of the lifting extension problem","intvolume":" 54","_id":"1073","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Submitted Version","scopus_import":"1","day":"01","article_processing_charge":"No","page":"915 - 965","publication":"Discrete & Computational Geometry","citation":{"mla":"Čadek, Martin, et al. “Algorithmic Solvability of the Lifting Extension Problem.” Discrete & Computational Geometry, vol. 54, no. 4, Springer, 2017, pp. 915–65, doi:10.1007/s00454-016-9855-6.","short":"M. Čadek, M. Krcál, L. Vokřínek, Discrete & Computational Geometry 54 (2017) 915–965.","chicago":"Čadek, Martin, Marek Krcál, and Lukáš Vokřínek. “Algorithmic Solvability of the Lifting Extension Problem.” Discrete & Computational Geometry. Springer, 2017. https://doi.org/10.1007/s00454-016-9855-6.","ama":"Čadek M, Krcál M, Vokřínek L. Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. 2017;54(4):915-965. doi:10.1007/s00454-016-9855-6","ista":"Čadek M, Krcál M, Vokřínek L. 2017. Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. 54(4), 915–965.","ieee":"M. Čadek, M. Krcál, and L. Vokřínek, “Algorithmic solvability of the lifting extension problem,” Discrete & Computational Geometry, vol. 54, no. 4. Springer, pp. 915–965, 2017.","apa":"Čadek, M., Krcál, M., & Vokřínek, L. (2017). Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9855-6"},"date_published":"2017-06-01T00:00:00Z"},{"type":"journal_article","abstract":[{"lang":"eng","text":"Let P be a finite point set in the plane. A cordinary triangle in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P . Motivated by a question of Erdös, and answering a question of de Zeeuw, we prove that there exists a constant c > 0such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(| P |). "}],"intvolume":" 66","title":"On the existence of ordinary triangles","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"793","oa_version":"Submitted Version","article_processing_charge":"No","day":"01","page":"28 - 31","citation":{"ama":"Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. On the existence of ordinary triangles. Computational Geometry: Theory and Applications. 2017;66:28-31. doi:10.1016/j.comgeo.2017.07.002","ista":"Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. 2017. On the existence of ordinary triangles. Computational Geometry: Theory and Applications. 66, 28–31.","apa":"Fulek, R., Mojarrad, H., Naszódi, M., Solymosi, J., Stich, S., & Szedlák, M. (2017). On the existence of ordinary triangles. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.07.002","ieee":"R. Fulek, H. Mojarrad, M. Naszódi, J. Solymosi, S. Stich, and M. Szedlák, “On the existence of ordinary triangles,” Computational Geometry: Theory and Applications, vol. 66. Elsevier, pp. 28–31, 2017.","mla":"Fulek, Radoslav, et al. “On the Existence of Ordinary Triangles.” Computational Geometry: Theory and Applications, vol. 66, Elsevier, 2017, pp. 28–31, doi:10.1016/j.comgeo.2017.07.002.","short":"R. Fulek, H. Mojarrad, M. Naszódi, J. Solymosi, S. Stich, M. Szedlák, Computational Geometry: Theory and Applications 66 (2017) 28–31.","chicago":"Fulek, Radoslav, Hossein Mojarrad, Márton Naszódi, József Solymosi, Sebastian Stich, and May Szedlák. “On the Existence of Ordinary Triangles.” Computational Geometry: Theory and Applications. Elsevier, 2017. https://doi.org/10.1016/j.comgeo.2017.07.002."},"publication":"Computational Geometry: Theory and Applications","date_published":"2017-01-01T00:00:00Z","publist_id":"6861","ec_funded":1,"department":[{"_id":"UlWa"}],"publisher":"Elsevier","publication_status":"published","year":"2017","volume":66,"date_created":"2018-12-11T11:48:32Z","date_updated":"2023-09-27T12:15:16Z","author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","first_name":"Radoslav","last_name":"Fulek","full_name":"Fulek, Radoslav"},{"full_name":"Mojarrad, Hossein","first_name":"Hossein","last_name":"Mojarrad"},{"last_name":"Naszódi","first_name":"Márton","full_name":"Naszódi, Márton"},{"last_name":"Solymosi","first_name":"József","full_name":"Solymosi, József"},{"full_name":"Stich, Sebastian","last_name":"Stich","first_name":"Sebastian"},{"full_name":"Szedlák, May","last_name":"Szedlák","first_name":"May"}],"publication_identifier":{"issn":["09257721"]},"month":"01","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"isi":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1701.08183","open_access":"1"}],"external_id":{"isi":["000412039700003"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2017.07.002"},{"page":"1 - 13","publication":"Computational Geometry: Theory and Applications","citation":{"chicago":"Fulek, Radoslav. “C-Planarity of Embedded Cyclic c-Graphs.” Computational Geometry: Theory and Applications. Elsevier, 2017. https://doi.org/10.1016/j.comgeo.2017.06.016.","mla":"Fulek, Radoslav. “C-Planarity of Embedded Cyclic c-Graphs.” Computational Geometry: Theory and Applications, vol. 66, Elsevier, 2017, pp. 1–13, doi:10.1016/j.comgeo.2017.06.016.","short":"R. Fulek, Computational Geometry: Theory and Applications 66 (2017) 1–13.","ista":"Fulek R. 2017. C-planarity of embedded cyclic c-graphs. Computational Geometry: Theory and Applications. 66, 1–13.","ieee":"R. Fulek, “C-planarity of embedded cyclic c-graphs,” Computational Geometry: Theory and Applications, vol. 66. Elsevier, pp. 1–13, 2017.","apa":"Fulek, R. (2017). C-planarity of embedded cyclic c-graphs. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.016","ama":"Fulek R. C-planarity of embedded cyclic c-graphs. Computational Geometry: Theory and Applications. 2017;66:1-13. doi:10.1016/j.comgeo.2017.06.016"},"date_published":"2017-12-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","title":"C-planarity of embedded cyclic c-graphs","status":"public","intvolume":" 66","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"794","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows. Given a graph G with the vertex set partitioned into three parts embedded on a 2-sphere, our algorithm decides if we can augment G by adding edges without creating an edge-crossing so that in the resulting spherical graph the vertices of each part induce a connected sub-graph. We proceed by a reduction to the problem of testing the existence of a perfect matching in planar bipartite graphs. We formulate our result in a slightly more general setting of cyclic clustered graphs, i.e., the simple graph obtained by contracting each cluster, where we disregard loops and multi-edges, is a cycle.","lang":"eng"}],"quality_controlled":"1","isi":1,"external_id":{"isi":["000412039700001"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1602.01346","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2017.06.016","month":"12","publication_status":"published","publisher":"Elsevier","department":[{"_id":"UlWa"}],"year":"2017","acknowledgement":"I would like to thank Jan Kynčl, Dömötör Pálvölgyi and anonymous referees for many comments and suggestions that helped to improve the presentation of the result.","date_updated":"2023-09-27T12:14:49Z","date_created":"2018-12-11T11:48:32Z","volume":66,"author":[{"first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"1165"}]},"publist_id":"6860"},{"day":"06","scopus_import":1,"series_title":"A Journey Through Discrete Mathematics","date_published":"2017-10-06T00:00:00Z","citation":{"ama":"Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. Bounding helly numbers via betti numbers. In: Loebl M, Nešetřil J, Thomas R, eds. A Journey through Discrete Mathematics: A Tribute to Jiri Matousek. A Journey Through Discrete Mathematics. Springer; 2017:407-447. doi:10.1007/978-3-319-44479-6_17","ieee":"X. Goaoc, P. Paták, Z. Patakova, M. Tancer, and U. Wagner, “Bounding helly numbers via betti numbers,” in A Journey through Discrete Mathematics: A Tribute to Jiri Matousek, M. Loebl, J. Nešetřil, and R. Thomas, Eds. Springer, 2017, pp. 407–447.","apa":"Goaoc, X., Paták, P., Patakova, Z., Tancer, M., & Wagner, U. (2017). Bounding helly numbers via betti numbers. In M. Loebl, J. Nešetřil, & R. Thomas (Eds.), A Journey through Discrete Mathematics: A Tribute to Jiri Matousek (pp. 407–447). Springer. https://doi.org/10.1007/978-3-319-44479-6_17","ista":"Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. 2017.Bounding helly numbers via betti numbers. In: A Journey through Discrete Mathematics: A Tribute to Jiri Matousek. , 407–447.","short":"X. Goaoc, P. Paták, Z. Patakova, M. Tancer, U. Wagner, in:, M. Loebl, J. Nešetřil, R. Thomas (Eds.), A Journey through Discrete Mathematics: A Tribute to Jiri Matousek, Springer, 2017, pp. 407–447.","mla":"Goaoc, Xavier, et al. “Bounding Helly Numbers via Betti Numbers.” A Journey through Discrete Mathematics: A Tribute to Jiri Matousek, edited by Martin Loebl et al., Springer, 2017, pp. 407–47, doi:10.1007/978-3-319-44479-6_17.","chicago":"Goaoc, Xavier, Pavel Paták, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Bounding Helly Numbers via Betti Numbers.” In A Journey through Discrete Mathematics: A Tribute to Jiri Matousek, edited by Martin Loebl, Jaroslav Nešetřil, and Robin Thomas, 407–47. A Journey Through Discrete Mathematics. Springer, 2017. https://doi.org/10.1007/978-3-319-44479-6_17."},"publication":"A Journey through Discrete Mathematics: A Tribute to Jiri Matousek","page":"407 - 447","abstract":[{"lang":"eng","text":"We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers b and d there exists an integer h(b, d) such that the following holds. If F is a finite family of subsets of Rd such that βi(∩G)≤b for any G⊊F and every 0 ≤ i ≤ [d/2]-1 then F has Helly number at most h(b, d). Here βi denotes the reduced Z2-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these [d/2] first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex K, some well-behaved chain map C*(K)→C*(Rd)."}],"type":"book_chapter","oa_version":"Published Version","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"424","status":"public","title":"Bounding helly numbers via betti numbers","publication_identifier":{"isbn":["978-331944479-6"]},"month":"10","doi":"10.1007/978-3-319-44479-6_17","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1310.4613v3"}],"oa":1,"quality_controlled":"1","publist_id":"7399","related_material":{"record":[{"id":"1512","status":"public","relation":"earlier_version"}]},"author":[{"last_name":"Goaoc","first_name":"Xavier","full_name":"Goaoc, Xavier"},{"full_name":"Paták, Pavel","first_name":"Pavel","last_name":"Paták"},{"full_name":"Patakova, Zuzana","last_name":"Patakova","first_name":"Zuzana","orcid":"0000-0002-3975-1683"},{"orcid":"0000-0002-1191-6714","last_name":"Tancer","first_name":"Martin","full_name":"Tancer, Martin"},{"full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"}],"date_created":"2018-12-11T11:46:24Z","date_updated":"2024-02-28T12:59:37Z","year":"2017","editor":[{"full_name":"Loebl, Martin","last_name":"Loebl","first_name":"Martin"},{"first_name":"Jaroslav","last_name":"Nešetřil","full_name":"Nešetřil, Jaroslav"},{"full_name":"Thomas, Robin","first_name":"Robin","last_name":"Thomas"}],"publisher":"Springer","department":[{"_id":"UlWa"}],"publication_status":"published"},{"abstract":[{"text":"Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher than 3. If such an operation is determined at the level of simplicial chains [see e.g. González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively computable. However, decomposing a cubical complex into a simplicial one deleteriously affects the efficiency of such an approach. In order to avoid this overhead, a direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015, 253-275] for the cup product in cohomology, and implemented in the ChainCon software package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series, 1947, 290-320] directly at the level of cubical chains, and we prove the correctness of this formula. An implementation of this formula is programmed in C++ within the ChainCon software framework. We provide a few examples and discuss the effectiveness of this approach. One specific application follows from the fact that Steenrod squares yield tests for the topological extension problem: Can a given map A → Sd to a sphere Sd be extended to a given super-complex X of A? In particular, the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"None","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1237","title":"Computation of cubical Steenrod squares","status":"public","intvolume":" 9667","day":"02","scopus_import":1,"date_published":"2016-06-02T00:00:00Z","citation":{"ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13","ieee":"M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented at the CTIC: Computational Topology in Image Context, Marseille, France, 2016, vol. 9667, pp. 140–151.","apa":"Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares (Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.","short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","mla":"Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares. Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.","chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13."},"page":"140 - 151","ec_funded":1,"publist_id":"6096","author":[{"first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"},{"full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T06:49:18Z","date_created":"2018-12-11T11:50:52Z","volume":9667,"acknowledgement":"The research conducted by both authors has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and no. 622033 (for P. P.).","year":"2016","publication_status":"published","publisher":"Springer","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"month":"06","conference":{"name":"CTIC: Computational Topology in Image Context","location":"Marseille, France","start_date":"2016-06-15","end_date":"2016-06-17"},"doi":"10.1007/978-3-319-39441-1_13","language":[{"iso":"eng"}],"quality_controlled":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"},{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7"}]},{"year":"2016","_id":"1282","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"}],"intvolume":" 216","publisher":"Springer","status":"public","publication_status":"published","title":"On eigenvalues of random complexes","author":[{"first_name":"Anna","last_name":"Gundert","full_name":"Gundert, Anna"},{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner"}],"volume":216,"oa_version":"Preprint","date_updated":"2021-01-12T06:49:36Z","date_created":"2018-12-11T11:51:07Z","type":"journal_article","issue":"2","publist_id":"6034","abstract":[{"lang":"eng","text":"We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial–Meshulam model Xk(n, p) of random k-dimensional simplicial complexes on n vertices. We show that for p = Ω(logn/n), the eigenvalues of each of the matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of (k - 2)-dimensional faces. Garland’s result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of k-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the eigenvalues of the higher-dimensional Laplacian capture the notion of coboundary expansion—a higher-dimensional generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov; this question was raised, for instance, by Dotterrer and Kahle. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every k ≥ 2 and n ∈ N, there is a k-dimensional complex Yn k on n vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised k-dimensional Laplacian lie in the interval [1−O(1/√1), 1+0(1/√1]) but whose coboundary expansion is bounded from above by O(log n/n) and so tends to zero as n → ∞; moreover, Yn k can be taken to have vanishing integer homology in dimension less than k."}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.4906"}],"oa":1,"citation":{"ista":"Gundert A, Wagner U. 2016. On eigenvalues of random complexes. Israel Journal of Mathematics. 216(2), 545–582.","apa":"Gundert, A., & Wagner, U. (2016). On eigenvalues of random complexes. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1419-1","ieee":"A. Gundert and U. Wagner, “On eigenvalues of random complexes,” Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 545–582, 2016.","ama":"Gundert A, Wagner U. On eigenvalues of random complexes. Israel Journal of Mathematics. 2016;216(2):545-582. doi:10.1007/s11856-016-1419-1","chicago":"Gundert, Anna, and Uli Wagner. “On Eigenvalues of Random Complexes.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1419-1.","mla":"Gundert, Anna, and Uli Wagner. “On Eigenvalues of Random Complexes.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016, pp. 545–82, doi:10.1007/s11856-016-1419-1.","short":"A. Gundert, U. Wagner, Israel Journal of Mathematics 216 (2016) 545–582."},"publication":"Israel Journal of Mathematics","page":"545 - 582","quality_controlled":"1","doi":"10.1007/s11856-016-1419-1","date_published":"2016-10-01T00:00:00Z","language":[{"iso":"eng"}],"scopus_import":1,"day":"01","month":"10"},{"abstract":[{"text":"A drawing in the plane (ℝ2) of a graph G = (V,E) equipped with a function γ : V → ℕ is x-bounded if (i) x(u) < x(v) whenever γ(u) < γ(v) and (ii) γ(u) ≤ γ(w) ≤ γ(v), where uv ∈ E and γ(u) ≤ γ(v), whenever x(w) ∈ x(uv), where x(.) denotes the projection to the xaxis.We prove a characterization of isotopy classes of embeddings of connected graphs equipped with γ in the plane containing an x-bounded embedding.Then we present an efficient algorithm, which relies on our result, for testing the existence of an x-bounded embedding if the given graph is a forest.This partially answers a question raised recently by Angelini et al.and Chang et al., and proves that c-planarity testing of flat clustered graphs with three clusters is tractable when the underlying abstract graph is a forest.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"Preprint","_id":"1348","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Bounded embeddings of graphs in the plane","intvolume":" 9843","day":"09","scopus_import":1,"date_published":"2016-08-09T00:00:00Z","citation":{"short":"R. Fulek, in:, Springer, 2016, pp. 31–42.","mla":"Fulek, Radoslav. Bounded Embeddings of Graphs in the Plane. Vol. 9843, Springer, 2016, pp. 31–42, doi:10.1007/978-3-319-44543-4_3.","chicago":"Fulek, Radoslav. “Bounded Embeddings of Graphs in the Plane,” 9843:31–42. Springer, 2016. https://doi.org/10.1007/978-3-319-44543-4_3.","ama":"Fulek R. Bounded embeddings of graphs in the plane. In: Vol 9843. Springer; 2016:31-42. doi:10.1007/978-3-319-44543-4_3","ieee":"R. Fulek, “Bounded embeddings of graphs in the plane,” presented at the IWOCA: International Workshop on Combinatorial Algorithms, Helsinki, Finland, 2016, vol. 9843, pp. 31–42.","apa":"Fulek, R. (2016). Bounded embeddings of graphs in the plane (Vol. 9843, pp. 31–42). Presented at the IWOCA: International Workshop on Combinatorial Algorithms, Helsinki, Finland: Springer. https://doi.org/10.1007/978-3-319-44543-4_3","ista":"Fulek R. 2016. Bounded embeddings of graphs in the plane. IWOCA: International Workshop on Combinatorial Algorithms, LNCS, vol. 9843, 31–42."},"page":"31 - 42","ec_funded":1,"publist_id":"5901","author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","first_name":"Radoslav","last_name":"Fulek","full_name":"Fulek, Radoslav"}],"date_created":"2018-12-11T11:51:31Z","date_updated":"2021-01-12T06:50:03Z","volume":9843,"year":"2016","publication_status":"published","publisher":"Springer","department":[{"_id":"UlWa"}],"month":"08","conference":{"name":"IWOCA: International Workshop on Combinatorial Algorithms","location":"Helsinki, Finland","start_date":"2016-08-17","end_date":"2018-08-19"},"doi":"10.1007/978-3-319-44543-4_3","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1610.07144"}],"oa":1,"quality_controlled":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}]},{"page":"51.1 - 51.12","citation":{"chicago":"Mabillard, Isaac, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the r-Metastable Range,” 51:51.1-51.12. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016. https://doi.org/10.4230/LIPIcs.SoCG.2016.51.","mla":"Mabillard, Isaac, and Uli Wagner. Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the r-Metastable Range. Vol. 51, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016, p. 51.1-51.12, doi:10.4230/LIPIcs.SoCG.2016.51.","short":"I. Mabillard, U. Wagner, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016, p. 51.1-51.12.","ista":"Mabillard I, Wagner U. 2016. Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 51, 51.1-51.12.","ieee":"I. Mabillard and U. Wagner, “Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range,” presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA, 2016, vol. 51, p. 51.1-51.12.","apa":"Mabillard, I., & Wagner, U. (2016). Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range (Vol. 51, p. 51.1-51.12). Presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH. https://doi.org/10.4230/LIPIcs.SoCG.2016.51","ama":"Mabillard I, Wagner U. Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range. In: Vol 51. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH; 2016:51.1-51.12. doi:10.4230/LIPIcs.SoCG.2016.51"},"date_published":"2016-06-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01","intvolume":" 51","title":"Eliminating higher-multiplicity intersections, II. The deleted product criterion in the r-metastable range","ddc":["510"],"status":"public","_id":"1381","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"date_created":"2018-12-12T10:10:06Z","date_updated":"2020-07-14T12:44:47Z","checksum":"92c0c3735fe908f8ded6e484005cb3b1","relation":"main_file","file_id":"4791","content_type":"application/pdf","file_size":622969,"creator":"system","file_name":"IST-2016-621-v1+1_LIPIcs-SoCG-2016-51.pdf","access_level":"open_access"}],"pubrep_id":"621","alternative_title":["LIPIcs"],"type":"conference","abstract":[{"text":"Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into double-struck Rd without higher-multiplicity intersections. We focus on conditions for the existence of almost r-embeddings, i.e., maps f : K → double-struck Rd such that f(σ1) ∩ ⋯ ∩ f(σr) = ∅ whenever σ1, ..., σr are pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber embeddability criterion, we show that a well-known necessary deleted product condition for the existence of almost r-embeddings is sufficient in a suitable r-metastable range of dimensions: If rd ≥ (r + 1) dim K + 3, then there exists an almost r-embedding K → double-struck Rd if and only if there exists an equivariant map (K)Δ r → Sr Sd(r-1)-1, where (K)Δ r is the deleted r-fold product of K, the target Sd(r-1)-1 is the sphere of dimension d(r - 1) - 1, and Sr is the symmetric group. This significantly extends one of the main results of our previous paper (which treated the special case where d = rk and dim K = (r - 1)k for some k ≥ 3), and settles an open question raised there.","lang":"eng"}],"project":[{"name":"Embeddings in Higher Dimensions: Algorithms and Combinatorics","_id":"25FA3206-B435-11E9-9278-68D0E5697425","grant_number":"PP00P2_138948"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2016.51","conference":{"start_date":"2016-06-14","location":"Medford, MA, USA","end_date":"2016-06-17","name":"SoCG: Symposium on Computational Geometry"},"month":"06","publisher":"Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH","department":[{"_id":"UlWa"}],"publication_status":"published","year":"2016","volume":51,"date_updated":"2021-01-12T06:50:17Z","date_created":"2018-12-11T11:51:41Z","author":[{"id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","last_name":"Mabillard","first_name":"Isaac","full_name":"Mabillard, Isaac"},{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"5830","file_date_updated":"2020-07-14T12:44:47Z"},{"ec_funded":1,"publist_id":"5799","file_date_updated":"2020-07-14T12:44:53Z","year":"2016","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","publisher":"Springer","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication_status":"published","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"1510"}]},"author":[{"first_name":"Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87","full_name":"Franek, Peter"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek","full_name":"Krcál, Marek"}],"volume":56,"date_created":"2018-12-11T11:51:51Z","date_updated":"2023-02-23T10:02:11Z","month":"07","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"_id":"25F8B9BC-B435-11E9-9278-68D0E5697425","grant_number":"M01980","name":"Robust invariants of Nonlinear Systems","call_identifier":"FWF"},{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","doi":"10.1007/s00454-016-9794-2","language":[{"iso":"eng"}],"type":"journal_article","issue":"1","abstract":[{"text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1408","intvolume":" 56","title":"On computability and triviality of well groups","ddc":["510"],"status":"public","pubrep_id":"614","oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":905303,"creator":"system","access_level":"open_access","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","checksum":"e0da023abf6b72abd8c6a8c76740d53c","date_created":"2018-12-12T10:10:55Z","date_updated":"2020-07-14T12:44:53Z","relation":"main_file","file_id":"4846"}],"scopus_import":1,"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","citation":{"chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:10.1007/s00454-016-9794-2.","short":"P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164.","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164, 2016.","apa":"Franek, P., & Krcál, M. (2016). On computability and triviality of well groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2","ama":"Franek P, Krcál M. On computability and triviality of well groups. Discrete & Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2"},"publication":"Discrete & Computational Geometry","page":"126 - 164","date_published":"2016-07-01T00:00:00Z"},{"publist_id":"5652","author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","first_name":"Serhii","full_name":"Avvakumov, Serhii"}],"volume":16,"date_created":"2018-12-11T11:52:30Z","date_updated":"2022-02-25T10:15:57Z","acknowledgement":"I thank A. Skopenkov for telling me about the problem and for his useful remarks. I also thank A. Sossinsky,\r\nA. Zhubr, M. Skopenkov, P. Akhmetiev, and an anonymous referee for their feedback. Author was partially\r\nsupported by Dobrushin fellowship, 2013, and by RFBR grant 15-01-06302.","year":"2016","publisher":"Independent University of Moscow","department":[{"_id":"UlWa"}],"publication_status":"published","publication_identifier":{"eissn":["1609-4514"]},"month":"01","doi":"10.17323/1609-4514-2016-16-1-1-25","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1408.3918"}],"oa":1,"external_id":{"arxiv":["1408.3918"]},"quality_controlled":"1","issue":"1","abstract":[{"text":"We classify smooth Brunnian (i.e., unknotted on both components) embeddings (S2 × S1) ⊔ S3 → ℝ6. Any Brunnian embedding (S2 × S1) ⊔ S3 → ℝ6 is isotopic to an explicitly constructed embedding fk,m,n for some integers k, m, n such that m ≡ n (mod 2). Two embeddings fk,m,n and fk′ ,m′,n′ are isotopic if and only if k = k′, m ≡ m′ (mod 2k) and n ≡ n′ (mod 2k). We use Haefliger’s classification of embeddings S3 ⊔ S3 → ℝ6 in our proof. The relation between the embeddings (S2 × S1) ⊔ S3 → ℝ6 and S3 ⊔ S3 → ℝ6 is not trivial, however. For example, we show that there exist embeddings f: (S2 ×S1) ⊔ S3 → ℝ6 and g, g′ : S3 ⊔ S3 → ℝ6 such that the componentwise embedded connected sum f # g is isotopic to f # g′ but g is not isotopic to g′.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1522","intvolume":" 16","status":"public","title":"The classification of certain linked 3-manifolds in 6-space","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2016-01-01T00:00:00Z","citation":{"ama":"Avvakumov S. The classification of certain linked 3-manifolds in 6-space. Moscow Mathematical Journal. 2016;16(1):1-25. doi:10.17323/1609-4514-2016-16-1-1-25","ista":"Avvakumov S. 2016. The classification of certain linked 3-manifolds in 6-space. Moscow Mathematical Journal. 16(1), 1–25.","apa":"Avvakumov, S. (2016). The classification of certain linked 3-manifolds in 6-space. Moscow Mathematical Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2016-16-1-1-25","ieee":"S. Avvakumov, “The classification of certain linked 3-manifolds in 6-space,” Moscow Mathematical Journal, vol. 16, no. 1. Independent University of Moscow, pp. 1–25, 2016.","mla":"Avvakumov, Sergey. “The Classification of Certain Linked 3-Manifolds in 6-Space.” Moscow Mathematical Journal, vol. 16, no. 1, Independent University of Moscow, 2016, pp. 1–25, doi:10.17323/1609-4514-2016-16-1-1-25.","short":"S. Avvakumov, Moscow Mathematical Journal 16 (2016) 1–25.","chicago":"Avvakumov, Sergey. “The Classification of Certain Linked 3-Manifolds in 6-Space.” Moscow Mathematical Journal. Independent University of Moscow, 2016. https://doi.org/10.17323/1609-4514-2016-16-1-1-25."},"publication":"Moscow Mathematical Journal","page":"1 - 25","article_type":"original"},{"oa_version":"Preprint","title":"On topological minors in random simplicial complexes","status":"public","intvolume":" 144","_id":"1523","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"For random graphs, the containment problem considers the probability that a binomial random graph G(n, p) contains a given graph as a substructure. When asking for the graph as a topological minor, i.e., for a copy of a subdivision of the given graph, it is well known that the (sharp) threshold is at p = 1/n. We consider a natural analogue of this question for higher-dimensional random complexes Xk(n, p), first studied by Cohen, Costa, Farber and Kappeler for k = 2. Improving previous results, we show that p = Θ(1/ √n) is the (coarse) threshold for containing a subdivision of any fixed complete 2-complex. For higher dimensions k > 2, we get that p = O(n−1/k) is an upper bound for the threshold probability of containing a subdivision of a fixed k-dimensional complex.","lang":"eng"}],"issue":"4","type":"journal_article","date_published":"2016-04-01T00:00:00Z","page":"1815 - 1828","publication":"Proceedings of the American Mathematical Society","citation":{"mla":"Gundert, Anna, and Uli Wagner. “On Topological Minors in Random Simplicial Complexes.” Proceedings of the American Mathematical Society, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1815–28, doi:10.1090/proc/12824.","short":"A. Gundert, U. Wagner, Proceedings of the American Mathematical Society 144 (2016) 1815–1828.","chicago":"Gundert, Anna, and Uli Wagner. “On Topological Minors in Random Simplicial Complexes.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12824.","ama":"Gundert A, Wagner U. On topological minors in random simplicial complexes. Proceedings of the American Mathematical Society. 2016;144(4):1815-1828. doi:10.1090/proc/12824","ista":"Gundert A, Wagner U. 2016. On topological minors in random simplicial complexes. Proceedings of the American Mathematical Society. 144(4), 1815–1828.","apa":"Gundert, A., & Wagner, U. (2016). On topological minors in random simplicial complexes. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/12824","ieee":"A. Gundert and U. Wagner, “On topological minors in random simplicial complexes,” Proceedings of the American Mathematical Society, vol. 144, no. 4. American Mathematical Society, pp. 1815–1828, 2016."},"day":"01","scopus_import":1,"date_created":"2018-12-11T11:52:30Z","date_updated":"2021-01-12T06:51:22Z","volume":144,"author":[{"full_name":"Gundert, Anna","last_name":"Gundert","first_name":"Anna"},{"full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"}],"publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"American Mathematical Society","year":"2016","acknowledgement":"This research was supported by the Swiss National Science Foundation (SNF Projects 200021-125309 and 200020-138230","publist_id":"5650","language":[{"iso":"eng"}],"doi":"10.1090/proc/12824","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1404.2106","open_access":"1"}],"oa":1,"month":"04"}]