[{"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","doi":"10.1007/978-3-031-49275-4_2","conference":{"name":"GD: Graph Drawing and Network Visualization","end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy","start_date":"2023-09-20"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0302-9743"],"isbn":["9783031492747"],"eissn":["1611-3349"]},"month":"01","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].","publisher":"Springer Nature","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication_status":"published","author":[{"first_name":"Phoebe","last_name":"De Nooijer","full_name":"De Nooijer, Phoebe"},{"last_name":"Terziadis","first_name":"Soeren","full_name":"Terziadis, Soeren"},{"full_name":"Weinberger, Alexandra","last_name":"Weinberger","first_name":"Alexandra"},{"full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mchedlidze, Tamara","last_name":"Mchedlidze","first_name":"Tamara"},{"last_name":"Löffler","first_name":"Maarten","full_name":"Löffler, Maarten"},{"last_name":"Rote","first_name":"Günter","full_name":"Rote, Günter"}],"volume":14466,"date_created":"2024-01-28T23:01:43Z","date_updated":"2024-01-29T09:45:06Z","citation":{"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","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.","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.","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","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.","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."},"publication":"31st International Symposium on Graph Drawing and Network Visualization","page":"18-33","date_published":"2024-01-06T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"06","_id":"14888","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 14466","title":"Removing popular faces in curve arrangements","status":"public","oa_version":"Preprint","type":"conference","alternative_title":["LNCS"],"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":["LIPIcs"],"abstract":[{"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).","lang":"eng"}],"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","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"15175","checksum":"0524d4189fd1ed08989546511343edf3","success":1,"date_created":"2024-03-25T07:44:30Z","date_updated":"2024-03-25T07:44:30Z","access_level":"open_access","file_name":"2024_LIPICs_Filakovsky.pdf","content_type":"application/pdf","file_size":927290,"creator":"dernst"}],"scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"No","publication":"41st International Symposium on Theoretical Aspects of Computer Science","citation":{"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.","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","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.","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","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.","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.","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."},"date_published":"2024-03-01T00:00:00Z","article_number":"34","file_date_updated":"2024-03-25T07:44:30Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","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","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"}],"author":[{"full_name":"Filakovský, Marek","last_name":"Filakovský","first_name":"Marek","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nakajima, Tamio Vesa","last_name":"Nakajima","first_name":"Tamio Vesa"},{"full_name":"Opršal, Jakub","first_name":"Jakub","last_name":"Opršal","id":"ec596741-c539-11ec-b829-c79322a91242","orcid":"0000-0003-1245-3456"},{"last_name":"Tasinato","first_name":"Gianluca","id":"0433290C-AF8F-11E9-A4C7-F729E6697425","full_name":"Tasinato, Gianluca"},{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli"}],"date_updated":"2024-03-25T07:45:54Z","date_created":"2024-03-24T23:00:59Z","volume":289,"month":"03","publication_identifier":{"isbn":["9783959773119"],"eissn":["1868-8969"]},"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":["2312.12981"]},"quality_controlled":"1","project":[{"name":"Algorithms for Embeddings and Homotopy Theory","call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425","grant_number":"P31312"},{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"conference":{"name":"STACS: Symposium on Theoretical Aspects of Computer Science","start_date":"2024-03-12","location":"Clermont-Ferrand, France","end_date":"2024-03-14"},"doi":"10.4230/LIPIcs.STACS.2024.34","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"doi":"10.1137/20m1378223","project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"isi":["000955000000001"],"arxiv":["2003.11351"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2003.11351","open_access":"1"}],"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"month":"01","volume":52,"date_updated":"2023-08-01T13:11:30Z","date_created":"2023-02-16T07:03:52Z","author":[{"full_name":"Krokhin, Andrei","last_name":"Krokhin","first_name":"Andrei"},{"last_name":"Opršal","first_name":"Jakub","orcid":"0000-0003-1245-3456","id":"ec596741-c539-11ec-b829-c79322a91242","full_name":"Opršal, Jakub"},{"first_name":"Marcin","last_name":"Wrochna","full_name":"Wrochna, Marcin"},{"first_name":"Stanislav","last_name":"Živný","full_name":"Živný, Stanislav"}],"department":[{"_id":"UlWa"}],"publisher":"Society for Industrial & Applied Mathematics","publication_status":"published","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. ","ec_funded":1,"date_published":"2023-01-01T00:00:00Z","page":"38-79","article_type":"original","citation":{"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","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.","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.","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."},"publication":"SIAM Journal on Computing","article_processing_charge":"No","day":"01","keyword":["General Mathematics","General Computer Science"],"scopus_import":"1","oa_version":"Preprint","intvolume":" 52","title":"Topology and adjunction in promise constraint satisfaction","status":"public","_id":"12563","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"1","abstract":[{"lang":"eng","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."}],"type":"journal_article"},{"file_date_updated":"2021-07-14T07:41:50Z","date_updated":"2023-08-14T11:26:34Z","date_created":"2021-07-14T07:01:28Z","volume":253,"author":[{"last_name":"Dymond","first_name":"Michael","full_name":"Dymond, Michael"},{"id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","orcid":"0000-0002-2512-8698","first_name":"Vojtech","last_name":"Kaluza","full_name":"Kaluza, Vojtech"}],"publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","year":"2023","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.","month":"03","publication_identifier":{"eissn":["1565-8511"]},"language":[{"iso":"eng"}],"doi":"10.1007/s11856-022-2448-6","quality_controlled":"1","isi":1,"external_id":{"isi":["000904950300003"],"arxiv":["1903.05923"]},"oa":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":[{"date_updated":"2021-07-14T07:41:50Z","date_created":"2021-07-14T07:41:50Z","checksum":"6fa0a3207dd1d6467c309fd1bcc867d1","file_id":"9653","relation":"main_file","creator":"vkaluza","file_size":900422,"content_type":"application/pdf","file_name":"separated_nets.pdf","access_level":"open_access"}],"ddc":["515","516"],"status":"public","title":"Highly irregular separated nets","intvolume":" 253","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9652","day":"01","has_accepted_license":"1","article_processing_charge":"No","keyword":["Lipschitz","bilipschitz","bounded displacement","modulus of continuity","separated net","non-realisable density","Burago--Kleiner construction"],"scopus_import":"1","date_published":"2023-03-01T00:00:00Z","article_type":"original","page":"501-554","publication":"Israel Journal of Mathematics","citation":{"ama":"Dymond M, Kaluza V. Highly irregular separated nets. Israel Journal of Mathematics. 2023;253:501-554. doi:10.1007/s11856-022-2448-6","ista":"Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal of Mathematics. 253, 501–554.","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","ieee":"M. Dymond and V. Kaluza, “Highly irregular separated nets,” Israel Journal of Mathematics, vol. 253. Springer Nature, pp. 501–554, 2023.","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.","short":"M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554.","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."}},{"file_date_updated":"2022-08-29T11:23:15Z","ec_funded":1,"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","publisher":"Springer Nature","department":[{"_id":"UlWa"}],"author":[{"last_name":"Arroyo Guevara","first_name":"Alan M","orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","full_name":"Arroyo Guevara, Alan M"},{"last_name":"Klute","first_name":"Fabian","full_name":"Klute, Fabian"},{"full_name":"Parada, Irene","first_name":"Irene","last_name":"Parada"},{"last_name":"Vogtenhuber","first_name":"Birgit","full_name":"Vogtenhuber, Birgit"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"},{"last_name":"Wiedera","first_name":"Tilo","full_name":"Wiedera, Tilo"}],"date_updated":"2023-08-14T12:51:25Z","date_created":"2022-08-28T22:02:01Z","volume":69,"month":"04","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"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,"quality_controlled":"1","isi":1,"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"doi":"10.1007/s00454-022-00394-9","language":[{"iso":"eng"}],"type":"journal_article","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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"11999","status":"public","title":"Inserting one edge into a simple drawing is hard","ddc":["510"],"intvolume":" 69","file":[{"file_name":"2022_DiscreteandComputionalGeometry_Arroyo.pdf","access_level":"open_access","creator":"alisjak","content_type":"application/pdf","file_size":1002218,"file_id":"12006","relation":"main_file","date_created":"2022-08-29T11:23:15Z","date_updated":"2022-08-29T11:23:15Z","success":1,"checksum":"def7ae3b28d9fd6aec16450e40090302"}],"oa_version":"Published Version","scopus_import":"1","day":"01","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","publication":"Discrete and Computational Geometry","citation":{"short":"A.M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, T. Wiedera, Discrete and Computational Geometry 69 (2023) 745–770.","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.","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","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.","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."},"article_type":"original","page":"745–770","date_published":"2023-04-01T00:00:00Z"},{"article_processing_charge":"Yes","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2023-07-01T00:00:00Z","citation":{"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","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.","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.","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."},"publication":"Journal of Graph Algorithms and Applications","page":"433-457","article_type":"original","issue":"6","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"file_size":865774,"content_type":"application/pdf","creator":"dernst","file_name":"2023_JourGraphAlgorithms_Arroyo.pdf","access_level":"open_access","date_updated":"2023-08-07T08:00:48Z","date_created":"2023-08-07T08:00:48Z","checksum":"9c30d2b8e324cc1c904f2aeec92013a3","success":1,"relation":"main_file","file_id":"13979"}],"_id":"13969","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 27","ddc":["510"],"title":"Approximating the bundled crossing number","status":"public","publication_identifier":{"issn":["1526-1719"]},"month":"07","doi":"10.7155/jgaa.00629","language":[{"iso":"eng"}],"external_id":{"arxiv":["2109.14892"]},"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":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","ec_funded":1,"file_date_updated":"2023-08-07T08:00:48Z","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"11185"}]},"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"},{"last_name":"Felsner","first_name":"Stefan","full_name":"Felsner, Stefan"}],"volume":27,"date_created":"2023-08-06T22:01:11Z","date_updated":"2023-09-25T10:56:10Z","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","department":[{"_id":"UlWa"}],"publisher":"Brown University","publication_status":"published"},{"has_accepted_license":"1","article_processing_charge":"No","day":"31","date_published":"2023-07-31T00:00:00Z","citation":{"ama":"Köse S. Exterior algebra and combinatorics. 2023. doi:10.15479/at:ista:13331","apa":"Köse, S. (2023). Exterior algebra and combinatorics. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:13331","ieee":"S. Köse, “Exterior algebra and combinatorics,” Institute of Science and Technology Austria, 2023.","ista":"Köse S. 2023. Exterior algebra and combinatorics. Institute of Science and Technology Austria.","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.","chicago":"Köse, Seyda. “Exterior Algebra and Combinatorics.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:13331."},"page":"26","abstract":[{"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","lang":"eng"}],"type":"dissertation","alternative_title":["ISTA Master's Thesis"],"oa_version":"Published Version","file":[{"file_name":"Exterior Algebra and Combinatorics.zip","access_level":"closed","creator":"skoese","content_type":"application/x-zip-compressed","file_size":28684,"file_id":"13333","relation":"source_file","date_updated":"2023-07-31T10:16:32Z","date_created":"2023-07-31T10:16:32Z","checksum":"96ee518d796d02af71395622c45de03c"},{"relation":"main_file","file_id":"13480","checksum":"f610f4713f88bc477de576aaa46b114e","success":1,"date_created":"2023-08-03T15:28:55Z","date_updated":"2023-08-03T15:28:55Z","access_level":"open_access","file_name":"thesis-pdfa.pdf","file_size":4953418,"content_type":"application/pdf","creator":"skoese"}],"_id":"13331","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","title":"Exterior algebra and combinatorics","ddc":["510","516"],"status":"public","publication_identifier":{"issn":["2791-4585"]},"month":"07","doi":"10.15479/at:ista:13331","language":[{"iso":"eng"}],"degree_awarded":"MS","supervisor":[{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner"}],"oa":1,"file_date_updated":"2023-08-03T15:28:55Z","related_material":{"record":[{"id":"12680","relation":"part_of_dissertation","status":"public"}]},"author":[{"full_name":"Köse, Seyda","id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb","last_name":"Köse","first_name":"Seyda"}],"date_created":"2023-07-31T10:20:55Z","date_updated":"2023-10-04T11:54:56Z","year":"2023","department":[{"_id":"GradSch"},{"_id":"UlWa"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published"},{"publication_identifier":{"issn":["0012-365X"]},"month":"06","quality_controlled":"1","external_id":{"arxiv":["2201.10892"]},"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2201.10892","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.disc.2023.113363","article_number":"113363","publisher":"Elsevier","department":[{"_id":"UlWa"},{"_id":"GradSch"}],"publication_status":"published","year":"2023","volume":346,"date_created":"2023-02-26T23:01:00Z","date_updated":"2023-10-04T11:54:57Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"13331"}]},"author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","first_name":"Grigory","last_name":"Ivanov"},{"id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb","last_name":"Köse","first_name":"Seyda","full_name":"Köse, Seyda"}],"scopus_import":"1","article_processing_charge":"No","day":"01","article_type":"letter_note","citation":{"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","ista":"Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 346(6), 113363.","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","ieee":"G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,” Discrete Mathematics, vol. 346, no. 6. Elsevier, 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.","short":"G. Ivanov, S. Köse, Discrete Mathematics 346 (2023).","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."},"publication":"Discrete Mathematics","date_published":"2023-06-01T00:00:00Z","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"}],"intvolume":" 346","status":"public","title":"Erdős-Ko-Rado and Hilton-Milner theorems for two-forms","_id":"12680","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint"},{"language":[{"iso":"eng"}],"date_published":"2023-12-04T00:00:00Z","doi":"10.1112/blms.12965","quality_controlled":"1","article_type":"original","publication":"Bulletin of the London Mathematical Society","citation":{"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.","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).","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","ama":"Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. 2023. doi:10.1112/blms.12965"},"oa":1,"main_file_link":[{"url":" https://doi.org/10.1112/blms.12965","open_access":"1"}],"external_id":{"arxiv":["2212.04308"]},"day":"04","month":"12","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"scopus_import":"1","date_updated":"2023-12-11T10:03:54Z","date_created":"2023-12-10T23:00:58Z","oa_version":"Published Version","author":[{"first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"},{"first_name":"Márton","last_name":"Naszódi","full_name":"Naszódi, Márton"}],"title":"Quantitative Steinitz theorem: A polynomial bound","publication_status":"epub_ahead","status":"public","publisher":"London Mathematical Society","department":[{"_id":"UlWa"}],"_id":"14660","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","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","abstract":[{"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.","lang":"eng"}],"type":"journal_article"},{"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"}],"author":[{"full_name":"Fulek, Radoslav","orcid":"0000-0001-8485-1774","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek","first_name":"Radoslav"},{"last_name":"Gärtner","first_name":"Bernd","full_name":"Gärtner, Bernd"},{"first_name":"Andrey","last_name":"Kupavskii","full_name":"Kupavskii, Andrey"},{"full_name":"Valtr, Pavel","last_name":"Valtr","first_name":"Pavel"},{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","full_name":"Wagner, Uli"}],"related_material":{"record":[{"id":"6647","status":"public","relation":"earlier_version"}]},"date_updated":"2023-12-13T12:03:35Z","date_created":"2023-08-06T22:01:12Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1812.04911","open_access":"1"}],"external_id":{"arxiv":["1812.04911"],"isi":["001038546500001"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"_id":"261FA626-B435-11E9-9278-68D0E5697425","grant_number":"M02281","call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs"}],"doi":"10.1007/s00454-023-00532-x","language":[{"iso":"eng"}],"month":"07","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13974","status":"public","title":"The crossing Tverberg theorem","oa_version":"Preprint","type":"journal_article","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."}],"publication":"Discrete and Computational Geometry","citation":{"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.","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.","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","ieee":"R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing Tverberg theorem,” Discrete and Computational Geometry. Springer Nature, 2023.","ista":"Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2023. The crossing Tverberg theorem. Discrete and Computational Geometry.","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"},"article_type":"original","date_published":"2023-07-27T00:00:00Z","scopus_import":"1","day":"27","article_processing_charge":"No"}]