--- _id: '14888' abstract: - lang: eng 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.' 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].' alternative_title: - LNCS article_processing_charge: No author: - first_name: Phoebe full_name: De Nooijer, Phoebe last_name: De Nooijer - first_name: Soeren full_name: Terziadis, Soeren last_name: Terziadis - first_name: Alexandra full_name: Weinberger, Alexandra last_name: Weinberger - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tamara full_name: Mchedlidze, Tamara last_name: Mchedlidze - first_name: Maarten full_name: Löffler, Maarten last_name: Löffler - first_name: Günter full_name: Rote, Günter last_name: Rote 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' 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' 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. 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.' 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. 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. conference: end_date: 2023-09-22 location: Isola delle Femmine, Palermo, Italy name: 'GD: Graph Drawing and Network Visualization' start_date: 2023-09-20 date_created: 2024-01-28T23:01:43Z date_published: 2024-01-06T00:00:00Z date_updated: 2024-01-29T09:45:06Z day: '06' department: - _id: UlWa - _id: HeEd doi: 10.1007/978-3-031-49275-4_2 external_id: arxiv: - '2202.12175' intvolume: ' 14466' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2202.12175 month: '01' oa: 1 oa_version: Preprint page: 18-33 publication: 31st International Symposium on Graph Drawing and Network Visualization publication_identifier: eissn: - 1611-3349 isbn: - '9783031492747' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Removing popular faces in curve arrangements type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14466 year: '2024' ... --- _id: '15168' 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).' 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)." alternative_title: - LIPIcs article_number: '34' article_processing_charge: No author: - first_name: Marek full_name: Filakovský, Marek id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87 last_name: Filakovský - first_name: Tamio Vesa full_name: Nakajima, Tamio Vesa last_name: Nakajima - first_name: Jakub full_name: Opršal, Jakub id: ec596741-c539-11ec-b829-c79322a91242 last_name: Opršal orcid: 0000-0003-1245-3456 - first_name: Gianluca full_name: Tasinato, Gianluca id: 0433290C-AF8F-11E9-A4C7-F729E6697425 last_name: Tasinato - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: 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' 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' 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. 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. 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.' 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. conference: end_date: 2024-03-14 location: Clermont-Ferrand, France name: 'STACS: Symposium on Theoretical Aspects of Computer Science' start_date: 2024-03-12 date_created: 2024-03-24T23:00:59Z date_published: 2024-03-01T00:00:00Z date_updated: 2024-03-25T07:45:54Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.STACS.2024.34 ec_funded: 1 external_id: arxiv: - '2312.12981' file: - access_level: open_access checksum: 0524d4189fd1ed08989546511343edf3 content_type: application/pdf creator: dernst date_created: 2024-03-25T07:44:30Z date_updated: 2024-03-25T07:44:30Z file_id: '15175' file_name: 2024_LIPICs_Filakovsky.pdf file_size: 927290 relation: main_file success: 1 file_date_updated: 2024-03-25T07:44:30Z has_accepted_license: '1' intvolume: ' 289' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '03' oa: 1 oa_version: Published Version project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: 41st International Symposium on Theoretical Aspects of Computer Science publication_identifier: eissn: - 1868-8969 isbn: - '9783959773119' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 289 year: '2024' ... --- _id: '12563' 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.' 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\x1Eects only the authors’ views and not the views of the ERC or the European Commission. " article_processing_charge: No article_type: original author: - first_name: Andrei full_name: Krokhin, Andrei last_name: Krokhin - first_name: Jakub full_name: Opršal, Jakub id: ec596741-c539-11ec-b829-c79322a91242 last_name: Opršal orcid: 0000-0003-1245-3456 - first_name: Marcin full_name: Wrochna, Marcin last_name: Wrochna - first_name: Stanislav full_name: Živný, Stanislav last_name: Živný 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 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 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. 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. 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. 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. short: A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52 (2023) 38–79. date_created: 2023-02-16T07:03:52Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-08-01T13:11:30Z day: '01' department: - _id: UlWa doi: 10.1137/20m1378223 ec_funded: 1 external_id: arxiv: - '2003.11351' isi: - '000955000000001' intvolume: ' 52' isi: 1 issue: '1' keyword: - General Mathematics - General Computer Science language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2003.11351 month: '01' oa: 1 oa_version: Preprint page: 38-79 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Topology and adjunction in promise constraint satisfaction type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 52 year: '2023' ... --- _id: '9652' 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. 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.' article_processing_charge: No article_type: original author: - first_name: Michael full_name: Dymond, Michael last_name: Dymond - first_name: Vojtech full_name: Kaluza, Vojtech id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E last_name: Kaluza orcid: 0000-0002-2512-8698 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 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 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. ieee: M. Dymond and V. Kaluza, “Highly irregular separated nets,” Israel Journal of Mathematics, vol. 253. Springer Nature, pp. 501–554, 2023. ista: Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal of Mathematics. 253, 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. short: M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554. date_created: 2021-07-14T07:01:28Z date_published: 2023-03-01T00:00:00Z date_updated: 2023-08-14T11:26:34Z day: '01' ddc: - '515' - '516' department: - _id: UlWa doi: 10.1007/s11856-022-2448-6 external_id: arxiv: - '1903.05923' isi: - '000904950300003' file: - access_level: open_access checksum: 6fa0a3207dd1d6467c309fd1bcc867d1 content_type: application/pdf creator: vkaluza date_created: 2021-07-14T07:41:50Z date_updated: 2021-07-14T07:41:50Z file_id: '9653' file_name: separated_nets.pdf file_size: 900422 relation: main_file file_date_updated: 2021-07-14T07:41:50Z has_accepted_license: '1' intvolume: ' 253' isi: 1 keyword: - Lipschitz - bilipschitz - bounded displacement - modulus of continuity - separated net - non-realisable density - Burago--Kleiner construction language: - iso: eng month: '03' oa: 1 oa_version: Submitted Version page: 501-554 publication: Israel Journal of Mathematics publication_identifier: eissn: - 1565-8511 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Highly irregular separated nets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 253 year: '2023' ... --- _id: '11999' 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.' 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.' article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Fabian full_name: Klute, Fabian last_name: Klute - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber - first_name: Raimund full_name: Seidel, Raimund last_name: Seidel - first_name: Tilo full_name: Wiedera, Tilo last_name: Wiedera citation: 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 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. 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. 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. date_created: 2022-08-28T22:02:01Z date_published: 2023-04-01T00:00:00Z date_updated: 2023-08-14T12:51:25Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1007/s00454-022-00394-9 ec_funded: 1 external_id: arxiv: - '1909.07347' isi: - '000840292800001' file: - access_level: open_access checksum: def7ae3b28d9fd6aec16450e40090302 content_type: application/pdf creator: alisjak date_created: 2022-08-29T11:23:15Z date_updated: 2022-08-29T11:23:15Z file_id: '12006' file_name: 2022_DiscreteandComputionalGeometry_Arroyo.pdf file_size: 1002218 relation: main_file success: 1 file_date_updated: 2022-08-29T11:23:15Z has_accepted_license: '1' intvolume: ' 69' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 745–770 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Inserting one edge into a simple drawing is hard tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 69 year: '2023' ... --- _id: '13969' 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." 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. article_processing_charge: Yes article_type: original author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Stefan full_name: Felsner, Stefan last_name: Felsner 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 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 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. 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. ista: Arroyo Guevara AM, Felsner S. 2023. Approximating the bundled crossing number. Journal of Graph Algorithms and Applications. 27(6), 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. short: A.M. Arroyo Guevara, S. Felsner, Journal of Graph Algorithms and Applications 27 (2023) 433–457. date_created: 2023-08-06T22:01:11Z date_published: 2023-07-01T00:00:00Z date_updated: 2023-09-25T10:56:10Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.7155/jgaa.00629 ec_funded: 1 external_id: arxiv: - '2109.14892' file: - access_level: open_access checksum: 9c30d2b8e324cc1c904f2aeec92013a3 content_type: application/pdf creator: dernst date_created: 2023-08-07T08:00:48Z date_updated: 2023-08-07T08:00:48Z file_id: '13979' file_name: 2023_JourGraphAlgorithms_Arroyo.pdf file_size: 865774 relation: main_file success: 1 file_date_updated: 2023-08-07T08:00:48Z has_accepted_license: '1' intvolume: ' 27' issue: '6' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 433-457 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Graph Algorithms and Applications publication_identifier: issn: - 1526-1719 publication_status: published publisher: Brown University quality_controlled: '1' related_material: record: - id: '11185' relation: earlier_version status: public scopus_import: '1' status: public title: Approximating the bundled crossing number tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 27 year: '2023' ... --- _id: '13331' 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" alternative_title: - ISTA Master's Thesis article_processing_charge: No author: - first_name: Seyda full_name: Köse, Seyda id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb last_name: Köse 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 chicago: Köse, Seyda. “Exterior Algebra and Combinatorics.” Institute of Science and Technology Austria, 2023. 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. mla: Köse, Seyda. Exterior Algebra and Combinatorics. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:13331. short: S. Köse, Exterior Algebra and Combinatorics, Institute of Science and Technology Austria, 2023. date_created: 2023-07-31T10:20:55Z date_published: 2023-07-31T00:00:00Z date_updated: 2023-10-04T11:54:56Z day: '31' ddc: - '510' - '516' degree_awarded: MS department: - _id: GradSch - _id: UlWa doi: 10.15479/at:ista:13331 file: - access_level: closed checksum: 96ee518d796d02af71395622c45de03c content_type: application/x-zip-compressed creator: skoese date_created: 2023-07-31T10:16:32Z date_updated: 2023-07-31T10:16:32Z file_id: '13333' file_name: Exterior Algebra and Combinatorics.zip file_size: 28684 relation: source_file - access_level: open_access checksum: f610f4713f88bc477de576aaa46b114e content_type: application/pdf creator: skoese date_created: 2023-08-03T15:28:55Z date_updated: 2023-08-03T15:28:55Z file_id: '13480' file_name: thesis-pdfa.pdf file_size: 4953418 relation: main_file success: 1 file_date_updated: 2023-08-03T15:28:55Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '26' publication_identifier: issn: - 2791-4585 publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '12680' relation: part_of_dissertation status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 title: Exterior algebra and combinatorics type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2023' ... --- _id: '12680' abstract: - lang: eng 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. article_number: '113363' article_processing_charge: No article_type: letter_note author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Seyda full_name: Köse, Seyda id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb last_name: Köse 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 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 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. ieee: G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,” Discrete Mathematics, vol. 346, no. 6. Elsevier, 2023. ista: Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 346(6), 113363. 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). date_created: 2023-02-26T23:01:00Z date_published: 2023-06-01T00:00:00Z date_updated: 2023-10-04T11:54:57Z day: '01' department: - _id: UlWa - _id: GradSch doi: 10.1016/j.disc.2023.113363 external_id: arxiv: - '2201.10892' intvolume: ' 346' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2201.10892' month: '06' oa: 1 oa_version: Preprint publication: Discrete Mathematics publication_identifier: issn: - 0012-365X publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '13331' relation: dissertation_contains status: public scopus_import: '1' status: public title: Erdős-Ko-Rado and Hilton-Milner theorems for two-forms type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 346 year: '2023' ... --- _id: '14660' abstract: - lang: eng text: "The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set \U0001D446⊂ℝ\U0001D451, then there are at most 2\U0001D451 points of \U0001D446 whose convex hull contains the origin in the interior. Bárány, Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem. Let \U0001D444 be a convex polytope in ℝ\U0001D451 containing the standard Euclidean unit ball \U0001D401\U0001D451. Then there exist at most 2\U0001D451 vertices of \U0001D444 whose convex hull \U0001D444′ satisfies \U0001D45F\U0001D401\U0001D451⊂\U0001D444′ with \U0001D45F⩾\U0001D451−2\U0001D451. They conjectured that \U0001D45F⩾\U0001D450\U0001D451−1∕2 holds with a universal constant \U0001D450>0. We prove \U0001D45F⩾15\U0001D4512, the first polynomial lower bound on \U0001D45F. Furthermore, we show that \U0001D45F is not greater than 2/√\U0001D451." 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 article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Márton full_name: Naszódi, Márton last_name: Naszódi citation: ama: 'Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society. 2023. doi:10.1112/blms.12965' 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' 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.' ieee: 'G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,” Bulletin of the London Mathematical Society. London Mathematical Society, 2023.' ista: 'Ivanov G, Naszódi M. 2023. Quantitative Steinitz theorem: A polynomial bound. Bulletin of the London Mathematical Society.' 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). date_created: 2023-12-10T23:00:58Z date_published: 2023-12-04T00:00:00Z date_updated: 2023-12-11T10:03:54Z day: '04' department: - _id: UlWa doi: 10.1112/blms.12965 external_id: arxiv: - '2212.04308' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.1112/blms.12965' month: '12' oa: 1 oa_version: Published Version publication: Bulletin of the London Mathematical Society publication_identifier: eissn: - 1469-2120 issn: - 0024-6093 publication_status: epub_ahead publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: 'Quantitative Steinitz theorem: A polynomial bound' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '13974' 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. 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)." article_processing_charge: No article_type: original author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Bernd full_name: Gärtner, Bernd last_name: Gärtner - first_name: Andrey full_name: Kupavskii, Andrey last_name: Kupavskii - first_name: Pavel full_name: Valtr, Pavel last_name: Valtr - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: 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 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 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. 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. mla: Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” Discrete and Computational Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00532-x. short: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, Discrete and Computational Geometry (2023). date_created: 2023-08-06T22:01:12Z date_published: 2023-07-27T00:00:00Z date_updated: 2023-12-13T12:03:35Z day: '27' department: - _id: UlWa doi: 10.1007/s00454-023-00532-x external_id: arxiv: - '1812.04911' isi: - '001038546500001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1812.04911 month: '07' oa: 1 oa_version: Preprint project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '6647' relation: earlier_version status: public scopus_import: '1' status: public title: The crossing Tverberg theorem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14445' 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." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Pascal full_name: Wild, Pascal id: 4C20D868-F248-11E8-B48F-1D18A9856A87 last_name: Wild citation: 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 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 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. 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. ista: Wagner U, Wild P. 2023. Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes. Israel Journal of Mathematics. 256(2), 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. short: U. Wagner, P. Wild, Israel Journal of Mathematics 256 (2023) 675–717. date_created: 2023-10-22T22:01:14Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-12-13T13:09:07Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1007/s11856-023-2521-9 external_id: isi: - '001081646400010' file: - access_level: open_access checksum: fbb05619fe4b650f341cc730425dd9c3 content_type: application/pdf creator: dernst date_created: 2023-10-31T11:20:31Z date_updated: 2023-10-31T11:20:31Z file_id: '14475' file_name: 2023_IsraelJourMath_Wagner.pdf file_size: 623787 relation: main_file success: 1 file_date_updated: 2023-10-31T11:20:31Z has_accepted_license: '1' intvolume: ' 256' isi: 1 issue: '2' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 675-717 publication: Israel Journal of Mathematics publication_identifier: eissn: - 1565-8511 issn: - 0021-2172 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 256 year: '2023' ... --- _id: '12833' 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.' 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" article_number: '9' article_processing_charge: No article_type: original author: - first_name: Ahmad full_name: Biniaz, Ahmad last_name: Biniaz - first_name: Kshitij full_name: Jain, Kshitij last_name: Jain - first_name: Anna full_name: Lubiw, Anna last_name: Lubiw - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tillmann full_name: Miltzow, Tillmann last_name: Miltzow - first_name: Debajyoti full_name: Mondal, Debajyoti last_name: Mondal - first_name: Anurag Murty full_name: Naredla, Anurag Murty last_name: Naredla - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Alexi full_name: Turcotte, Alexi last_name: Turcotte citation: 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 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 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. ieee: A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 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. 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). date_created: 2023-04-16T22:01:08Z date_published: 2023-01-18T00:00:00Z date_updated: 2024-01-04T12:42:09Z day: '18' ddc: - '000' department: - _id: KrCh - _id: HeEd - _id: UlWa doi: 10.46298/DMTCS.8383 external_id: arxiv: - '1903.06981' file: - access_level: open_access checksum: 439102ea4f6e2aeefd7107dfb9ccf532 content_type: application/pdf creator: dernst date_created: 2023-04-17T08:10:28Z date_updated: 2023-04-17T08:10:28Z file_id: '12844' file_name: 2022_DMTCS_Biniaz.pdf file_size: 2072197 relation: main_file success: 1 file_date_updated: 2023-04-17T08:10:28Z has_accepted_license: '1' intvolume: ' 24' issue: '2' language: - iso: eng month: '01' oa: 1 oa_version: Published Version publication: Discrete Mathematics and Theoretical Computer Science publication_identifier: eissn: - 1365-8050 issn: - 1462-7264 publication_status: published publisher: EPI Sciences quality_controlled: '1' related_material: record: - id: '7950' relation: earlier_version status: public scopus_import: '1' status: public title: Token swapping on trees tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '14737' abstract: - lang: eng 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.' 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.]." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Márton full_name: Naszódi, Márton last_name: Naszódi citation: 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 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 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. 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. 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. 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. date_created: 2024-01-08T09:48:56Z date_published: 2023-12-01T00:00:00Z date_updated: 2024-01-08T09:57:25Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1093/imrn/rnad210 external_id: arxiv: - '2212.11781' file: - access_level: open_access checksum: 353666cea80633beb0f1ffd342dff6d4 content_type: application/pdf creator: dernst date_created: 2024-01-08T09:53:09Z date_updated: 2024-01-08T09:53:09Z file_id: '14738' file_name: 2023_IMRN_Ivanov.pdf file_size: 815777 relation: main_file success: 1 file_date_updated: 2024-01-08T09:53:09Z has_accepted_license: '1' intvolume: ' 2023' issue: '23' keyword: - General Mathematics language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '12' oa: 1 oa_version: Published Version page: 20613-20669 publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' status: public title: Functional John and Löwner conditions for pairs of log-concave functions tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2023 year: '2023' ... --- _id: '9651' 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. 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.' article_number: '15' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Michael full_name: Dymond, Michael last_name: Dymond - first_name: Vojtech full_name: Kaluza, Vojtech id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E last_name: Kaluza orcid: 0000-0002-2512-8698 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 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 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. ieee: M. Dymond and V. Kaluza, “Divergence of separated nets with respect to displacement equivalence,” Geometriae Dedicata. Springer Nature, 2023. ista: Dymond M, Kaluza V. 2023. Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata., 15. 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. short: M. Dymond, V. Kaluza, Geometriae Dedicata (2023). date_created: 2021-07-14T07:01:27Z date_published: 2023-11-17T00:00:00Z date_updated: 2024-01-11T13:06:32Z day: '17' department: - _id: UlWa doi: 10.1007/s10711-023-00862-3 external_id: arxiv: - '2102.13046' isi: - '001105681500001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s10711-023-00862-3 month: '11' oa: 1 oa_version: Published Version publication: Geometriae Dedicata publication_identifier: eissn: - 1572-9168 issn: - 0046-5755 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Divergence of separated nets with respect to displacement equivalence type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '13270' 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." acknowledgement: Open access funding provided by the Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Florestan R full_name: Brunck, Florestan R id: 6ab6e556-f394-11eb-9cf6-9dfb78f00d8d last_name: Brunck citation: 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 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 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. 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. 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. short: F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089. date_created: 2023-07-23T22:01:14Z date_published: 2023-07-05T00:00:00Z date_updated: 2024-01-29T11:16:16Z day: '05' ddc: - '510' department: - _id: UlWa doi: 10.1007/s00454-023-00500-5 external_id: arxiv: - '2107.04112' isi: - '001023742800003' file: - access_level: open_access checksum: 865e68daafdd4edcfc280172ec50f5ea content_type: application/pdf creator: dernst date_created: 2024-01-29T11:15:22Z date_updated: 2024-01-29T11:15:22Z file_id: '14897' file_name: 2023_DiscreteComputGeometry_Brunck.pdf file_size: 1466020 relation: main_file success: 1 file_date_updated: 2024-01-29T11:15:22Z has_accepted_license: '1' intvolume: ' 70' isi: 1 issue: '3' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 1059-1089 publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Iterated medial triangle subdivision in surfaces of constant curvature tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 70 year: '2023' ... --- _id: '11991' 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. article_processing_charge: No article_type: original author: - first_name: Andrei full_name: Krokhin, Andrei last_name: Krokhin - first_name: Jakub full_name: Opršal, Jakub id: ec596741-c539-11ec-b829-c79322a91242 last_name: Opršal orcid: 0000-0003-1245-3456 citation: 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 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 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. 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. ista: Krokhin A, Opršal J. 2022. An invitation to the promise constraint satisfaction problem. ACM SIGLOG News. 9(3), 30–59. 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. date_created: 2022-08-27T11:23:37Z date_published: 2022-07-01T00:00:00Z date_updated: 2022-09-05T08:19:38Z day: '01' department: - _id: UlWa doi: 10.1145/3559736.3559740 external_id: arxiv: - '2208.13538' intvolume: ' 9' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/2208.13538 month: '07' oa: 1 oa_version: Preprint page: 30-59 publication: ACM SIGLOG News publication_identifier: issn: - 2372-3491 publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' status: public title: An invitation to the promise constraint satisfaction problem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 9 year: '2022' ... --- _id: '11938' abstract: - lang: eng 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. 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).' article_processing_charge: No article_type: original author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Daniel full_name: Perz, Daniel last_name: Perz - first_name: Alexander full_name: Pilz, Alexander last_name: Pilz - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: 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 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 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. ieee: O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022. 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. 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. 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. date_created: 2022-08-21T22:01:56Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-02-23T13:54:21Z day: '01' ddc: - '000' department: - _id: UlWa - _id: HeEd - _id: KrCh doi: 10.7155/jgaa.00591 ec_funded: 1 external_id: arxiv: - '2101.03928' file: - access_level: open_access checksum: dc6e255e3558faff924fd9e370886c11 content_type: application/pdf creator: dernst date_created: 2022-08-22T06:42:42Z date_updated: 2022-08-22T06:42:42Z file_id: '11940' file_name: 2022_JourGraphAlgorithmsApplic_Aichholzer.pdf file_size: 694538 relation: main_file success: 1 file_date_updated: 2022-08-22T06:42:42Z has_accepted_license: '1' intvolume: ' 26' issue: '2' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 225-240 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: Journal of Graph Algorithms and Applications publication_identifier: issn: - 1526-1719 publication_status: published publisher: Brown University quality_controlled: '1' related_material: record: - id: '9296' relation: earlier_version status: public scopus_import: '1' status: public title: On compatible matchings tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2022' ... --- _id: '11777' abstract: - lang: eng 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." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Pascal full_name: Wild, Pascal id: 4C20D868-F248-11E8-B48F-1D18A9856A87 last_name: Wild citation: ama: Wild P. High-dimensional expansion and crossing numbers of simplicial complexes. 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 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. 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. mla: Wild, Pascal. High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes. Institute of Science and Technology, 2022, doi:10.15479/at:ista:11777. short: P. Wild, High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes, Institute of Science and Technology, 2022. date_created: 2022-08-10T15:51:19Z date_published: 2022-08-11T00:00:00Z date_updated: 2023-06-22T09:56:36Z day: '11' ddc: - '500' - '516' - '514' degree_awarded: PhD department: - _id: GradSch - _id: UlWa doi: 10.15479/at:ista:11777 ec_funded: 1 file: - access_level: open_access checksum: f5f3af1fb7c8a24b71ddc88ad7f7c5b4 content_type: text/x-python creator: pwild date_created: 2022-08-10T15:34:04Z date_updated: 2022-08-10T15:34:04Z description: Code for computer-assisted proofs in Section 8.4.7 in Thesis file_id: '11780' file_name: flags.py file_size: 16828 relation: supplementary_material - access_level: open_access checksum: 1f7c12dfe3bdaa9b147e4fbc3d34e3d5 content_type: text/x-c++src creator: pwild date_created: 2022-08-10T15:34:10Z date_updated: 2022-08-10T15:34:10Z description: Code for proof of Lemma 8.20 in Thesis file_id: '11781' file_name: lowerbound.cpp file_size: 12226 relation: supplementary_material - access_level: open_access checksum: 4cf81455c49e5dec3b9b2e3980137eeb content_type: text/x-python creator: pwild date_created: 2022-08-10T15:34:17Z date_updated: 2022-08-10T15:34:17Z description: Code for proof of Proposition 7.9 in Thesis file_id: '11782' file_name: upperbound.py file_size: 3240 relation: supplementary_material - access_level: open_access checksum: 4e96575b10cbe4e0d0db2045b2847774 content_type: application/pdf creator: pwild date_created: 2022-08-11T16:08:33Z date_updated: 2022-08-11T16:08:33Z file_id: '11809' file_name: finalthesisPascalWildPDFA.pdf file_size: 5086282 relation: main_file title: High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes - access_level: closed checksum: 92d94842a1fb6dca5808448137573b2e content_type: application/zip creator: pwild date_created: 2022-08-11T16:09:19Z date_updated: 2022-08-11T16:09:19Z file_id: '11810' file_name: ThesisSubmission.zip file_size: 18150068 relation: source_file file_date_updated: 2022-08-11T16:09:19Z has_accepted_license: '1' language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: '170' project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication_identifier: isbn: - 978-3-99078-021-3 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 title: High-dimensional expansion and crossing numbers of simplicial complexes type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2022' ... --- _id: '10335' 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." 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.' article_processing_charge: No article_type: original author: - first_name: Vojtech full_name: Kaluza, Vojtech id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E last_name: Kaluza orcid: 0000-0002-2512-8698 - first_name: Martin full_name: Tancer, Martin id: 38AC689C-F248-11E8-B48F-1D18A9856A87 last_name: Tancer orcid: 0000-0002-1191-6714 citation: 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 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 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. 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. ista: Kaluza V, Tancer M. 2022. Even maps, the Colin de Verdière number and representations of graphs. Combinatorica. 42, 1317–1345. 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. date_created: 2021-11-25T13:49:16Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-02T06:43:27Z day: '01' ddc: - '514' - '516' department: - _id: UlWa doi: 10.1007/s00493-021-4443-7 external_id: arxiv: - '1907.05055' isi: - '000798210100003' intvolume: ' 42' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.1907.05055' month: '12' oa: 1 oa_version: Preprint page: 1317-1345 publication: Combinatorica publication_identifier: issn: - 0209-9683 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Even maps, the Colin de Verdière number and representations of graphs type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 42 year: '2022' ... --- _id: '10776' 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.' 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. article_processing_charge: No article_type: original author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 - first_name: Martin full_name: Tancer, Martin last_name: Tancer - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 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 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 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. 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. ista: Patakova Z, Tancer M, Wagner U. 2022. Barycentric cuts through a convex body. Discrete and Computational Geometry. 68, 1133–1154. 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. date_created: 2022-02-20T23:01:35Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-02T14:38:58Z day: '01' department: - _id: UlWa doi: 10.1007/s00454-021-00364-7 external_id: arxiv: - '2003.13536' isi: - '000750681500001' intvolume: ' 68' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2003.13536 month: '12' oa: 1 oa_version: Preprint page: 1133-1154 publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Barycentric cuts through a convex body type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 68 year: '2022' ... --- _id: '10887' abstract: - lang: eng 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." 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. ' article_number: '109441' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Márton full_name: Naszódi, Márton last_name: Naszódi citation: ama: Ivanov G, Naszódi M. Functional John ellipsoids. Journal of Functional Analysis. 2022;282(11). doi:10.1016/j.jfa.2022.109441 apa: Ivanov, G., & Naszódi, M. (2022). Functional John ellipsoids. Journal of Functional Analysis. Elsevier. https://doi.org/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. ieee: G. Ivanov and M. Naszódi, “Functional John ellipsoids,” Journal of Functional Analysis, vol. 282, no. 11. Elsevier, 2022. ista: Ivanov G, Naszódi M. 2022. Functional John ellipsoids. Journal of Functional Analysis. 282(11), 109441. 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. short: G. Ivanov, M. Naszódi, Journal of Functional Analysis 282 (2022). date_created: 2022-03-20T23:01:38Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-08-02T14:51:11Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1016/j.jfa.2022.109441 external_id: arxiv: - '2006.09934' isi: - '000781371300008' file: - access_level: open_access checksum: 1cf185e264e04c87cb1ce67a00db88ab content_type: application/pdf creator: dernst date_created: 2022-08-02T10:40:48Z date_updated: 2022-08-02T10:40:48Z file_id: '11721' file_name: 2022_JourFunctionalAnalysis_Ivanov.pdf file_size: 734482 relation: main_file success: 1 file_date_updated: 2022-08-02T10:40:48Z has_accepted_license: '1' intvolume: ' 282' isi: 1 issue: '11' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Functional John ellipsoids tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 282 year: '2022' ... --- _id: '12129' abstract: - lang: eng 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.' 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" article_processing_charge: No article_type: original author: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Emo full_name: Welzl, Emo last_name: Welzl citation: 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 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 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. 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. ista: Wagner U, Welzl E. 2022. Connectivity of triangulation flip graphs in the plane. Discrete & Computational Geometry. 68(4), 1227–1284. 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. date_created: 2023-01-12T12:02:28Z date_published: 2022-11-14T00:00:00Z date_updated: 2023-08-04T08:51:08Z day: '14' ddc: - '510' department: - _id: UlWa doi: 10.1007/s00454-022-00436-2 external_id: isi: - '000883222200003' file: - access_level: open_access checksum: 307e879d09e52eddf5b225d0aaa9213a content_type: application/pdf creator: dernst date_created: 2023-01-23T11:10:03Z date_updated: 2023-01-23T11:10:03Z file_id: '12345' file_name: 2022_DiscreteCompGeometry_Wagner.pdf file_size: 1747581 relation: main_file success: 1 file_date_updated: 2023-01-23T11:10:03Z has_accepted_license: '1' intvolume: ' 68' isi: 1 issue: '4' keyword: - Computational Theory and Mathematics - Discrete Mathematics and Combinatorics - Geometry and Topology - Theoretical Computer Science language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 1227-1284 publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '7807' relation: earlier_version status: public - id: '7990' relation: earlier_version status: public scopus_import: '1' status: public title: Connectivity of triangulation flip graphs in the plane tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 68 year: '2022' ... --- _id: '11593' 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 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.' 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." article_processing_charge: No article_type: original author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Jan full_name: Kynčl, Jan last_name: Kynčl citation: 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 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 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. ieee: R. Fulek and J. Kynčl, “The Z2-Genus of Kuratowski minors,” Discrete and Computational Geometry, vol. 68. Springer Nature, pp. 425–447, 2022. ista: Fulek R, Kynčl J. 2022. The Z2-Genus of Kuratowski minors. Discrete and Computational Geometry. 68, 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. short: R. Fulek, J. Kynčl, Discrete and Computational Geometry 68 (2022) 425–447. date_created: 2022-07-17T22:01:56Z date_published: 2022-09-01T00:00:00Z date_updated: 2023-08-14T12:43:52Z day: '01' department: - _id: UlWa doi: 10.1007/s00454-022-00412-w external_id: arxiv: - '1803.05085' isi: - '000825014500001' intvolume: ' 68' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1803.05085 month: '09' oa: 1 oa_version: Preprint page: 425-447 project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '186' relation: earlier_version status: public scopus_import: '1' status: public title: The Z2-Genus of Kuratowski minors type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 68 year: '2022' ... --- _id: '11185' abstract: - lang: eng 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. 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. article_processing_charge: No author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Stefan full_name: Felsner, Stefan last_name: Felsner 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' 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' 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.' 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.' 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.' 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.' short: 'A.M. Arroyo Guevara, S. Felsner, in:, WALCOM 2022: Algorithms and Computation, Springer Nature, 2022, pp. 383–395.' conference: end_date: 2022-03-26 location: Jember, Indonesia name: 'WALCOM: Algorithms and Computation' start_date: 2022-03-24 date_created: 2022-04-17T22:01:47Z date_published: 2022-03-16T00:00:00Z date_updated: 2023-09-25T10:56:10Z day: '16' department: - _id: UlWa doi: 10.1007/978-3-030-96731-4_31 ec_funded: 1 external_id: arxiv: - '2109.14892' intvolume: ' 13174' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2109.14892' month: '03' oa: 1 oa_version: Preprint page: 383-395 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 'WALCOM 2022: Algorithms and Computation' publication_identifier: eissn: - 1611-3349 isbn: - '9783030967307' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '13969' relation: later_version status: public scopus_import: '1' series_title: LNCS status: public title: Approximating the bundled crossing number type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 13174 year: '2022' ... --- _id: '14381' 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. article_processing_charge: No article_type: original author: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: 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 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 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. 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. ista: Wagner U. 2022. High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others). Bulletin de la Societe Mathematique de France. 438, 281–294. 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. date_created: 2023-10-01T22:01:14Z date_published: 2022-01-01T00:00:00Z date_updated: 2023-10-03T08:04:03Z day: '01' department: - _id: UlWa doi: 10.24033/ast.1188 intvolume: ' 438' language: - iso: eng month: '01' oa_version: None page: 281-294 publication: Bulletin de la Societe Mathematique de France publication_identifier: eissn: - 2102-622X issn: - 0037-9484 publication_status: published publisher: Societe Mathematique de France quality_controlled: '1' scopus_import: '1' status: public title: High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 438 year: '2022' ... --- _id: '11435' abstract: - lang: eng 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 $Q \subset - 8d^3 Q^{\prime \prime}.$' 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." article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Marton full_name: Naszodi, Marton last_name: Naszodi citation: 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' 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' 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.' 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.' ista: 'Ivanov G, Naszodi M. 2022. A quantitative Helly-type theorem: Containment in a homothet. SIAM Journal on Discrete Mathematics. 36(2), 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.' short: G. Ivanov, M. Naszodi, SIAM Journal on Discrete Mathematics 36 (2022) 951–957. date_created: 2022-06-05T22:01:50Z date_published: 2022-04-11T00:00:00Z date_updated: 2023-10-18T06:58:03Z day: '11' department: - _id: UlWa doi: 10.1137/21M1403308 external_id: arxiv: - '2103.04122' isi: - '000793158200002' intvolume: ' 36' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2103.04122' month: '04' oa: 1 oa_version: Preprint page: 951-957 publication: SIAM Journal on Discrete Mathematics publication_identifier: issn: - 0895-4801 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: 'A quantitative Helly-type theorem: Containment in a homothet' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 36 year: '2022' ... --- _id: '9296' 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.' 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).' alternative_title: - LNCS article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Daniel full_name: Perz, Daniel last_name: Perz - first_name: Alexander full_name: Pilz, Alexander last_name: Pilz - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber 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' 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' 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. ieee: O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233. 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.' 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. 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. conference: end_date: 2021-03-02 location: Yangon, Myanmar name: 'WALCOM: Algorithms and Computation' start_date: 2021-02-28 date_created: 2021-03-28T22:01:41Z date_published: 2021-02-16T00:00:00Z date_updated: 2023-02-21T16:33:44Z day: '16' department: - _id: UlWa - _id: HeEd - _id: KrCh doi: 10.1007/978-3-030-68211-8_18 ec_funded: 1 external_id: arxiv: - '2101.03928' intvolume: ' 12635' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2101.03928 month: '02' oa: 1 oa_version: Preprint page: 221-233 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: 15th International Conference on Algorithms and Computation publication_identifier: eissn: - '16113349' isbn: - '9783030682101' issn: - '03029743' publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '11938' relation: later_version status: public scopus_import: '1' status: public title: On compatible matchings type: conference user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 12635 year: '2021' ... --- _id: '9037' 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 \U0001D700 ‐net theorem in Banach spaces of type \U0001D45D>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." 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." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov 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 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. 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. 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. short: G. Ivanov, Bulletin of the London Mathematical Society 53 (2021) 631–641. date_created: 2021-01-24T23:01:08Z date_published: 2021-04-01T00:00:00Z date_updated: 2023-08-07T13:35:20Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.1112/blms.12449 external_id: arxiv: - '1912.08561' isi: - '000607265100001' file: - access_level: open_access checksum: e6ceaa6470d835eb4c211cbdd38fdfd1 content_type: application/pdf creator: kschuh date_created: 2021-08-06T09:59:45Z date_updated: 2021-08-06T09:59:45Z file_id: '9796' file_name: 2021_BLMS_Ivanov.pdf file_size: 194550 relation: main_file success: 1 file_date_updated: 2021-08-06T09:59:45Z has_accepted_license: '1' intvolume: ' 53' isi: 1 issue: '2' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 631-641 publication: Bulletin of the London Mathematical Society publication_identifier: eissn: - '14692120' issn: - '00246093' publication_status: published publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 53 year: '2021' ... --- _id: '9098' abstract: - lang: eng 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." 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' article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov citation: ama: Ivanov G. On the volume of projections of the cross-polytope. Discrete Mathematics. 2021;344(5). 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 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. 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. 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. short: G. Ivanov, Discrete Mathematics 344 (2021). date_created: 2021-02-07T23:01:12Z date_published: 2021-05-01T00:00:00Z date_updated: 2023-08-07T13:40:37Z day: '01' department: - _id: UlWa doi: 10.1016/j.disc.2021.112312 external_id: arxiv: - '1808.09165' isi: - '000633365200001' intvolume: ' 344' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1808.09165 month: '05' oa: 1 oa_version: Preprint publication: Discrete Mathematics publication_identifier: issn: - 0012365X publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: On the volume of projections of the cross-polytope type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 344 year: '2021' ... --- _id: '9295' abstract: - lang: eng text: "Hill's Conjecture states that the crossing number cr(\U0001D43E\U0001D45B) \ of the complete graph \U0001D43E\U0001D45B in the plane (equivalently, the sphere) is 14⌊\U0001D45B2⌋⌊\U0001D45B−12⌋⌊\U0001D45B−22⌋⌊\U0001D45B−32⌋=\U0001D45B4/64+\U0001D442(\U0001D45B3) . 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 \ \U0001D45B4/64+\U0001D442(\U0001D45B3) , thus matching asymptotically the conjectured value of cr(\U0001D43E\U0001D45B) . Let cr\U0001D443(\U0001D43A) denote the crossing number of a graph \U0001D43A in the projective plane. Recently, Elkies proved that the expected number of crossings in a naturally defined random projective plane drawing of \U0001D43E\U0001D45B is (\U0001D45B4/8\U0001D70B2)+\U0001D442(\U0001D45B3) . In analogy with the relation of Moon's result to Hill's conjecture, Elkies asked if lim\U0001D45B→∞ cr\U0001D443(\U0001D43E\U0001D45B)/\U0001D45B4=1/8\U0001D70B2 . We construct drawings of \U0001D43E\U0001D45B in the projective plane that disprove this." 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." article_processing_charge: No article_type: original author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Dan full_name: Mcquillan, Dan last_name: Mcquillan - first_name: R. Bruce full_name: Richter, R. Bruce last_name: Richter - first_name: Gelasio full_name: Salazar, Gelasio last_name: Salazar - first_name: Matthew full_name: Sullivan, Matthew last_name: Sullivan citation: 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 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 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. 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. 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. 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. short: A.M. Arroyo Guevara, D. Mcquillan, R.B. Richter, G. Salazar, M. Sullivan, Journal of Graph Theory 97 (2021) 426–440. date_created: 2021-03-28T22:01:41Z date_published: 2021-03-23T00:00:00Z date_updated: 2023-08-07T14:26:15Z day: '23' department: - _id: UlWa doi: 10.1002/jgt.22665 ec_funded: 1 external_id: arxiv: - '2002.02287' isi: - '000631693200001' intvolume: ' 97' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2002.02287 month: '03' oa: 1 oa_version: Preprint page: 426-440 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Graph Theory publication_identifier: eissn: - 1097-0118 issn: - 0364-9024 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Drawings of complete graphs in the projective plane type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 97 year: '2021' ... --- _id: '9468' 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" article_processing_charge: No article_type: original author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: R. Bruce full_name: Richter, R. Bruce last_name: Richter - first_name: Matthew full_name: Sunohara, Matthew last_name: Sunohara citation: 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 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 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. 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. 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. 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. date_created: 2021-06-06T22:01:30Z date_published: 2021-05-20T00:00:00Z date_updated: 2023-08-08T13:58:12Z day: '20' department: - _id: UlWa doi: 10.1137/20M1313234 ec_funded: 1 external_id: arxiv: - '2001.06053' isi: - '000674142200022' intvolume: ' 35' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2001.06053 month: '05' oa: 1 oa_version: Preprint page: 1050-1076 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: SIAM Journal on Discrete Mathematics publication_identifier: issn: - '08954801' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Extending drawings of complete graphs into arrangements of pseudocircles type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 35 year: '2021' ... --- _id: '9548' 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.' acknowledgement: The authors acknowledge the support of the grant of the Russian Government N 075-15-2019-1926. article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Igor full_name: Tsiutsiurupa, Igor last_name: Tsiutsiurupa citation: ama: Ivanov G, Tsiutsiurupa I. Functional Löwner ellipsoids. Journal of Geometric Analysis. 2021;31:11493-11528. doi:10.1007/s12220-021-00691-4 apa: Ivanov, G., & Tsiutsiurupa, I. (2021). Functional Löwner ellipsoids. Journal of Geometric Analysis. Springer. https://doi.org/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. 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. 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. short: G. Ivanov, I. Tsiutsiurupa, Journal of Geometric Analysis 31 (2021) 11493–11528. date_created: 2021-06-13T22:01:32Z date_published: 2021-05-31T00:00:00Z date_updated: 2023-08-08T14:04:49Z day: '31' department: - _id: UlWa doi: 10.1007/s12220-021-00691-4 external_id: arxiv: - '2008.09543' isi: - '000656507500001' intvolume: ' 31' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2008.09543 month: '05' oa: 1 oa_version: Preprint page: 11493-11528 publication: Journal of Geometric Analysis publication_identifier: eissn: - 1559-002X issn: - 1050-6926 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Functional Löwner ellipsoids type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 31 year: '2021' ... --- _id: '10181' abstract: - lang: eng 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. acknowledgement: Theorem 2 was obtained at Steklov Mathematical Institute RAS and supported by Russian Science Foundation, grant N 19-11-00087. article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Mariana S. full_name: Lopushanski, Mariana S. last_name: Lopushanski citation: ama: Ivanov G, Lopushanski MS. Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis. 2021. doi:10.1007/s11228-021-00612-1 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 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. ieee: G. Ivanov and M. S. Lopushanski, “Rectifiable curves in proximally smooth sets,” Set-Valued and Variational Analysis. Springer Nature, 2021. ista: Ivanov G, Lopushanski MS. 2021. Rectifiable curves in proximally smooth sets. Set-Valued and Variational Analysis. 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. short: G. Ivanov, M.S. Lopushanski, Set-Valued and Variational Analysis (2021). date_created: 2021-10-24T22:01:35Z date_published: 2021-10-09T00:00:00Z date_updated: 2023-08-14T08:11:38Z day: '09' department: - _id: UlWa doi: 10.1007/s11228-021-00612-1 external_id: arxiv: - '2012.10691' isi: - '000705774800001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2012.10691 month: '10' oa: 1 oa_version: Published Version publication: Set-Valued and Variational Analysis publication_identifier: eissn: - 1877-0541 issn: - 0927-6947 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Rectifiable curves in proximally smooth sets type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '10220' abstract: - lang: eng 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." 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. article_processing_charge: No article_type: original author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Isaac full_name: Mabillard, Isaac id: 32BF9DAA-F248-11E8-B48F-1D18A9856A87 last_name: Mabillard - first_name: Arkadiy B. full_name: Skopenkov, Arkadiy B. last_name: Skopenkov - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 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 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 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. 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. ista: Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. 2021. Eliminating higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics. 245, 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. short: S. Avvakumov, I. Mabillard, A.B. Skopenkov, U. Wagner, Israel Journal of Mathematics 245 (2021) 501–534. date_created: 2021-11-07T23:01:24Z date_published: 2021-10-30T00:00:00Z date_updated: 2023-08-14T11:43:55Z day: '30' department: - _id: UlWa doi: 10.1007/s11856-021-2216-z external_id: arxiv: - '1511.03501' isi: - '000712942100013' intvolume: ' 245' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1511.03501 month: '10' oa: 1 oa_version: Preprint page: '501–534 ' project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: Israel Journal of Mathematics publication_identifier: eissn: - 1565-8511 issn: - 0021-2172 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '8183' relation: earlier_version status: public - id: '9308' relation: earlier_version status: public scopus_import: '1' status: public title: Eliminating higher-multiplicity intersections. III. Codimension 2 type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 245 year: '2021' ... --- _id: '10856' 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 \x1Cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2." 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." article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Igor full_name: Tsiutsiurupa, Igor last_name: Tsiutsiurupa 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 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 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. 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. ista: Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18. 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. date_created: 2022-03-18T09:25:14Z date_published: 2021-01-29T00:00:00Z date_updated: 2023-08-17T07:07:58Z day: '29' ddc: - '510' department: - _id: UlWa doi: 10.1515/agms-2020-0103 external_id: arxiv: - '2004.02674' isi: - '000734286800001' file: - access_level: open_access checksum: 7e615ac8489f5eae580b6517debfdc53 content_type: application/pdf creator: dernst date_created: 2022-03-18T09:31:59Z date_updated: 2022-03-18T09:31:59Z file_id: '10857' file_name: 2021_AnalysisMetricSpaces_Ivanov.pdf file_size: 789801 relation: main_file success: 1 file_date_updated: 2022-03-18T09:31:59Z has_accepted_license: '1' intvolume: ' 9' isi: 1 issue: '1' keyword: - Applied Mathematics - Geometry and Topology - Analysis language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 1-18 publication: Analysis and Geometry in Metric Spaces publication_identifier: issn: - 2299-3274 publication_status: published publisher: De Gruyter quality_controlled: '1' scopus_import: '1' status: public title: On the volume of sections of the cube tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ... --- _id: '10860' abstract: - lang: eng 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. 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. article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov citation: ama: Ivanov G. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 2021;64(4):942-963. doi:10.4153/s000843952000096x apa: Ivanov, G. (2021). Tight frames and related geometric problems. Canadian Mathematical Bulletin. Canadian Mathematical Society. https://doi.org/10.4153/s000843952000096x chicago: Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin. Canadian Mathematical Society, 2021. 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. ista: Ivanov G. 2021. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 64(4), 942–963. 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. date_created: 2022-03-18T09:55:59Z date_published: 2021-12-18T00:00:00Z date_updated: 2023-09-05T12:43:09Z day: '18' department: - _id: UlWa doi: 10.4153/s000843952000096x external_id: arxiv: - '1804.10055' isi: - '000730165300021' intvolume: ' 64' isi: 1 issue: '4' keyword: - General Mathematics - Tight frame - Grassmannian - zonotope language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.10055 month: '12' oa: 1 oa_version: Preprint page: 942-963 publication: Canadian Mathematical Bulletin publication_identifier: eissn: - 1496-4287 issn: - 0008-4395 publication_status: published publisher: Canadian Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Tight frames and related geometric problems type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 64 year: '2021' ... --- _id: '7806' abstract: - lang: eng 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." article_processing_charge: No author: - first_name: Marek full_name: Filakovský, Marek id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87 last_name: Filakovský - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Stephan Y full_name: Zhechev, Stephan Y id: 3AA52972-F248-11E8-B48F-1D18A9856A87 last_name: Zhechev citation: 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' 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' 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. 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. 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.' 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. short: M. Filakovský, U. Wagner, S.Y. Zhechev, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2020, pp. 767–785. conference: end_date: 2020-01-08 location: Salt Lake City, UT, United States name: 'SODA: Symposium on Discrete Algorithms' start_date: 2020-01-05 date_created: 2020-05-10T22:00:48Z date_published: 2020-01-01T00:00:00Z date_updated: 2021-01-12T08:15:38Z day: '01' department: - _id: UlWa doi: 10.1137/1.9781611975994.47 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1137/1.9781611975994.47 month: '01' oa: 1 oa_version: Published Version page: 767-785 project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: isbn: - '9781611975994' publication_status: published publisher: SIAM quality_controlled: '1' scopus_import: 1 status: public title: Embeddability of simplicial complexes is undecidable type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2020-January year: '2020' ... --- _id: '7991' abstract: - lang: eng 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.' alternative_title: - LIPIcs article_number: 12:1 - 12:15 article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Gabriel full_name: Nivasch, Gabriel last_name: Nivasch citation: 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' 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' 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. 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. 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.' 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. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:19Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:23Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.12 external_id: arxiv: - '1909.00263' file: - access_level: open_access checksum: 6872df6549142f709fb6354a1b2f2c06 content_type: application/pdf creator: dernst date_created: 2020-06-23T11:13:49Z date_updated: 2020-07-14T12:48:06Z file_id: '8007' file_name: 2020_LIPIcsSoCG_Avvakumov.pdf file_size: 575896 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng license: https://creativecommons.org/licenses/by/3.0/ month: '06' oa: 1 oa_version: Published Version project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Homotopic curve shortening and the affine curve-shortening flow tmp: image: /images/cc_by.png 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) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7989' abstract: - lang: eng 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.' alternative_title: - LIPIcs article_number: 61:1-61:13 article_processing_charge: No author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 citation: 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' 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' 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. ieee: Z. Patakova, “Bounding radon number via Betti numbers,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. 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.' 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. short: Z. Patakova, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:18Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:22Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.61 external_id: arxiv: - '1908.01677' file: - access_level: open_access checksum: d0996ca5f6eb32ce955ce782b4f2afbe content_type: application/pdf creator: dernst date_created: 2020-06-23T06:56:23Z date_updated: 2020-07-14T12:48:06Z file_id: '8005' file_name: 2020_LIPIcsSoCG_Patakova_61.pdf file_size: 645421 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Bounding radon number via Betti numbers tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7992' 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 article_number: 62:1 - 62:16 article_processing_charge: No author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 - first_name: Martin full_name: Tancer, Martin id: 38AC689C-F248-11E8-B48F-1D18A9856A87 last_name: Tancer orcid: 0000-0002-1191-6714 - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: 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' 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' 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. 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. 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.' 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. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:20Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:23Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.62 external_id: arxiv: - '2003.13536' file: - access_level: open_access checksum: ce1c9194139a664fb59d1efdfc88eaae content_type: application/pdf creator: dernst date_created: 2020-06-23T06:45:52Z date_updated: 2020-07-14T12:48:06Z file_id: '8004' file_name: 2020_LIPIcsSoCG_Patakova.pdf file_size: 750318 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Barycentric cuts through a convex body tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7994' abstract: - lang: eng 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. alternative_title: - LIPIcs article_number: 9:1 - 9:14 article_processing_charge: No author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Julien full_name: Bensmail, Julien last_name: Bensmail - first_name: R. full_name: Bruce Richter, R. last_name: Bruce Richter citation: 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' 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' 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. 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. 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.' 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. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:21Z date_published: 2020-06-01T00:00:00Z date_updated: 2023-02-23T13:22:12Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.9 ec_funded: 1 external_id: arxiv: - '1804.09317' file: - access_level: open_access checksum: 93571b76cf97d5b7c8aabaeaa694dd7e content_type: application/pdf creator: dernst date_created: 2020-06-23T11:06:23Z date_updated: 2020-07-14T12:48:06Z file_id: '8006' file_name: 2020_LIPIcsSoCG_Arroyo.pdf file_size: 592661 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Extending drawings of graphs to arrangements of pseudolines tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7990' 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).' alternative_title: - LIPIcs article_number: 67:1 - 67:16 article_processing_charge: No author: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Emo full_name: Welzl, Emo last_name: Welzl citation: 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' 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' 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.' 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.' 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.' 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. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:19Z date_published: 2020-06-01T00:00:00Z date_updated: 2023-08-04T08:51:07Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.67 external_id: arxiv: - '2003.13557' file: - access_level: open_access checksum: 3f6925be5f3dcdb3b14cab92f410edf7 content_type: application/pdf creator: dernst date_created: 2020-06-23T06:37:27Z date_updated: 2020-07-14T12:48:06Z file_id: '8003' file_name: 2020_LIPIcsSoCG_Wagner.pdf file_size: 793187 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '12129' relation: later_version status: public scopus_import: 1 status: public title: 'Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips)' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7807' 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." article_processing_charge: No author: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Emo full_name: Welzl, Emo last_name: Welzl citation: 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' 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' 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.' 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.' 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.' 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. conference: end_date: 2020-01-08 location: Salt Lake City, UT, United States name: 'SODA: Symposium on Discrete Algorithms' start_date: 2020-01-05 date_created: 2020-05-10T22:00:48Z date_published: 2020-01-01T00:00:00Z date_updated: 2023-08-04T08:51:07Z day: '01' department: - _id: UlWa doi: 10.1137/1.9781611975994.172 external_id: arxiv: - '2003.13557' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1137/1.9781611975994.172 month: '01' oa: 1 oa_version: Submitted Version page: 2823-2841 publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: isbn: - '9781611975994' publication_status: published publisher: SIAM quality_controlled: '1' related_material: record: - id: '12129' relation: later_version status: public scopus_import: 1 status: public title: 'Connectivity of triangulation flip graphs in the plane (Part I: Edge flips)' type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2020-January year: '2020' ... --- _id: '9308' acknowledgement: This research was carried out with the support of the Russian Foundation for Basic Research(grant no. 19-01-00169) article_processing_charge: No article_type: original author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Isaac full_name: Mabillard, Isaac id: 32BF9DAA-F248-11E8-B48F-1D18A9856A87 last_name: Mabillard - first_name: A. B. full_name: Skopenkov, A. B. last_name: Skopenkov citation: 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 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 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. 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. ista: Avvakumov S, Wagner U, Mabillard I, Skopenkov AB. 2020. Eliminating higher-multiplicity intersections, III. Codimension 2. Russian Mathematical Surveys. 75(6), 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. short: S. Avvakumov, U. Wagner, I. Mabillard, A.B. Skopenkov, Russian Mathematical Surveys 75 (2020) 1156–1158. date_created: 2021-04-04T22:01:22Z date_published: 2020-12-01T00:00:00Z date_updated: 2023-08-14T11:43:54Z day: '01' department: - _id: UlWa doi: 10.1070/RM9943 external_id: arxiv: - '1511.03501' isi: - '000625983100001' intvolume: ' 75' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1511.03501 month: '12' oa: 1 oa_version: Preprint page: 1156-1158 publication: Russian Mathematical Surveys publication_identifier: issn: - 0036-0279 publication_status: published publisher: IOP Publishing quality_controlled: '1' related_material: record: - id: '8183' relation: earlier_version status: public - id: '10220' relation: later_version status: public scopus_import: '1' status: public title: Eliminating higher-multiplicity intersections, III. Codimension 2 type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 75 year: '2020' ... --- _id: '6563' abstract: - lang: eng text: "This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps \U0001D453,\U0001D454:\U0001D44B→\U0001D44C, and the second computes the group [\U0001D6F4\U0001D44B,\U0001D44C]∗ 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 \U0001D434⊆\U0001D44B." article_processing_charge: No article_type: original author: - first_name: Marek full_name: Filakovský, Marek id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87 last_name: Filakovský - first_name: Lukas full_name: Vokřínek, Lukas last_name: Vokřínek citation: 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 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 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. 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. ista: Filakovský M, Vokřínek L. 2020. Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. 20, 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. short: M. Filakovský, L. Vokřínek, Foundations of Computational Mathematics 20 (2020) 311–330. date_created: 2019-06-16T21:59:14Z date_published: 2020-04-01T00:00:00Z date_updated: 2023-08-17T13:50:44Z day: '01' department: - _id: UlWa doi: 10.1007/s10208-019-09419-x external_id: arxiv: - '1312.2337' isi: - '000522437400004' intvolume: ' 20' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1312.2337 month: '04' oa: 1 oa_version: Preprint page: 311-330 project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: Foundations of Computational Mathematics publication_identifier: eissn: - '16153383' issn: - '16153375' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Are two given maps homotopic? An algorithmic viewpoint type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 20 year: '2020' ... --- _id: '7960' 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. 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." article_processing_charge: No article_type: original author: - first_name: Gil full_name: Kalai, Gil last_name: Kalai - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 citation: 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 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 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. ieee: G. Kalai and Z. Patakova, “Intersection patterns of planar sets,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 304–323, 2020. ista: Kalai G, Patakova Z. 2020. Intersection patterns of planar sets. Discrete and Computational Geometry. 64, 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. short: G. Kalai, Z. Patakova, Discrete and Computational Geometry 64 (2020) 304–323. date_created: 2020-06-14T22:00:50Z date_published: 2020-09-01T00:00:00Z date_updated: 2023-08-21T08:26:34Z day: '01' department: - _id: UlWa doi: 10.1007/s00454-020-00205-z external_id: arxiv: - '1907.00885' isi: - '000537329400001' intvolume: ' 64' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1907.00885 month: '09' oa: 1 oa_version: Preprint page: 304-323 publication: Discrete and Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Intersection patterns of planar sets type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 64 year: '2020' ... --- _id: '8732' 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.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Fabian full_name: Klute, Fabian last_name: Klute - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Raimund full_name: Seidel, Raimund last_name: Seidel - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber - first_name: Tilo full_name: Wiedera, Tilo last_name: Wiedera citation: 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' 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' 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. 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. 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.' 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. 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. conference: end_date: 2020-06-26 location: Leeds, United Kingdom name: 'WG: Workshop on Graph-Theoretic Concepts in Computer Science' start_date: 2020-06-24 date_created: 2020-11-06T08:45:03Z date_published: 2020-10-09T00:00:00Z date_updated: 2023-09-05T15:09:16Z day: '09' department: - _id: UlWa doi: 10.1007/978-3-030-60440-0_26 ec_funded: 1 intvolume: ' 12301' language: - iso: eng month: '10' oa_version: None page: 325-338 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Graph-Theoretic Concepts in Computer Science publication_identifier: eissn: - 1611-3349 isbn: - '9783030604394' - '9783030604400' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Inserting one edge into a simple drawing is hard type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 12301 year: '2020' ... --- _id: '7944' abstract: - lang: eng 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." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 citation: ama: Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944 apa: Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944 chicago: Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944. ieee: Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020. ista: Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria. 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. date_created: 2020-06-08T00:49:46Z date_published: 2020-06-09T00:00:00Z date_updated: 2023-09-07T13:17:37Z day: '09' ddc: - '516' - '514' degree_awarded: PhD department: - _id: HeEd - _id: UlWa doi: 10.15479/AT:ISTA:7944 file: - access_level: open_access checksum: df688bc5a82b50baee0b99d25fc7b7f0 content_type: application/pdf creator: zmasarov date_created: 2020-06-08T00:34:00Z date_updated: 2020-07-14T12:48:05Z file_id: '7945' file_name: THESIS_Zuzka_Masarova.pdf file_size: 13661779 relation: main_file - access_level: closed checksum: 45341a35b8f5529c74010b7af43ac188 content_type: application/zip creator: zmasarov date_created: 2020-06-08T00:35:30Z date_updated: 2020-07-14T12:48:05Z file_id: '7946' file_name: THESIS_Zuzka_Masarova_SOURCE_FILES.zip file_size: 32184006 relation: source_file file_date_updated: 2020-07-14T12:48:05Z has_accepted_license: '1' keyword: - reconfiguration - reconfiguration graph - triangulations - flip - constrained triangulations - shellability - piecewise-linear balls - token swapping - trees - coloured weighted token swapping language: - iso: eng license: https://creativecommons.org/licenses/by-sa/4.0/ month: '06' oa: 1 oa_version: Published Version page: '160' publication_identifier: isbn: - 978-3-99078-005-3 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '7950' relation: part_of_dissertation status: public - id: '5986' relation: part_of_dissertation status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: Reconfiguration problems tmp: image: /images/cc_by_sa.png legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) short: CC BY-SA (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _id: '8032' 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." acknowledged_ssus: - _id: E-Lib - _id: CampIT alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Kristóf full_name: Huszár, Kristóf id: 33C26278-F248-11E8-B48F-1D18A9856A87 last_name: Huszár orcid: 0000-0002-5445-5057 citation: ama: Huszár K. Combinatorial width parameters for 3-dimensional manifolds. 2020. doi:10.15479/AT:ISTA:8032 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 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. ieee: K. Huszár, “Combinatorial width parameters for 3-dimensional manifolds,” Institute of Science and Technology Austria, 2020. ista: Huszár K. 2020. Combinatorial width parameters for 3-dimensional manifolds. Institute of Science and Technology Austria. 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. date_created: 2020-06-26T10:00:36Z date_published: 2020-06-26T00:00:00Z date_updated: 2023-09-07T13:18:27Z day: '26' ddc: - '514' degree_awarded: PhD department: - _id: UlWa doi: 10.15479/AT:ISTA:8032 file: - access_level: open_access checksum: bd8be6e4f1addc863dfcc0fad29ee9c3 content_type: application/pdf creator: khuszar date_created: 2020-06-26T10:03:58Z date_updated: 2020-07-14T12:48:08Z file_id: '8034' file_name: Kristof_Huszar-Thesis.pdf file_size: 2637562 relation: main_file - access_level: closed checksum: d5f8456202b32f4a77552ef47a2837d1 content_type: application/x-zip-compressed creator: khuszar date_created: 2020-06-26T10:10:06Z date_updated: 2020-07-14T12:48:08Z file_id: '8035' file_name: Kristof_Huszar-Thesis-source.zip file_size: 7163491 relation: source_file file_date_updated: 2020-07-14T12:48:08Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: xviii+120 publication_identifier: isbn: - 978-3-99078-006-0 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '6556' relation: dissertation_contains status: public - id: '7093' relation: dissertation_contains status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Jonathan full_name: Spreer, Jonathan last_name: Spreer title: Combinatorial width parameters for 3-dimensional manifolds tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _id: '8156' 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.' alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov citation: ama: Avvakumov S. Topological methods in geometry and discrete mathematics. 2020. doi:10.15479/AT:ISTA:8156 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 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. ieee: S. Avvakumov, “Topological methods in geometry and discrete mathematics,” Institute of Science and Technology Austria, 2020. ista: Avvakumov S. 2020. Topological methods in geometry and discrete mathematics. Institute of Science and Technology Austria. 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. date_created: 2020-07-23T09:51:29Z date_published: 2020-07-24T00:00:00Z date_updated: 2023-12-18T10:51:01Z day: '24' ddc: - '514' degree_awarded: PhD department: - _id: UlWa doi: 10.15479/AT:ISTA:8156 file: - access_level: closed content_type: application/zip creator: savvakum date_created: 2020-07-27T12:44:51Z date_updated: 2020-07-27T12:44:51Z file_id: '8178' file_name: source.zip file_size: 1061740 relation: source_file - access_level: open_access content_type: application/pdf creator: savvakum date_created: 2020-07-27T12:46:53Z date_updated: 2020-07-27T12:46:53Z file_id: '8179' file_name: thesis_pdfa.pdf file_size: 1336501 relation: main_file success: 1 file_date_updated: 2020-07-27T12:46:53Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '119' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '8182' relation: part_of_dissertation status: public - id: '8183' relation: part_of_dissertation status: public - id: '8185' relation: part_of_dissertation status: public - id: '8184' relation: part_of_dissertation status: public - id: '6355' relation: part_of_dissertation status: public - id: '75' relation: part_of_dissertation status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 title: Topological methods in geometry and discrete mathematics type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ...