{"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959773119"]},"year":"2024","ddc":["510"],"abstract":[{"text":"A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, … , k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the \"linearly ordered chromatic number\" of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).","lang":"eng"}],"department":[{"_id":"UlWa"}],"oa_version":"Published Version","ec_funded":1,"status":"public","has_accepted_license":"1","date_created":"2024-03-24T23:00:59Z","article_number":"34","type":"conference","citation":{"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 <i>41st International Symposium on Theoretical Aspects of Computer Science</i>, Vol. 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">https://doi.org/10.4230/LIPIcs.STACS.2024.34</a>.","apa":"Filakovský, M., Nakajima, T. V., Opršal, J., Tasinato, G., &#38; Wagner, U. (2024). Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In <i>41st International Symposium on Theoretical Aspects of Computer Science</i> (Vol. 289). Clermont-Ferrand, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">https://doi.org/10.4230/LIPIcs.STACS.2024.34</a>","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.","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.","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 <i>41st International Symposium on Theoretical Aspects of Computer Science</i>, Clermont-Ferrand, France, 2024, vol. 289.","ama":"Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In: <i>41st International Symposium on Theoretical Aspects of Computer Science</i>. Vol 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">10.4230/LIPIcs.STACS.2024.34</a>","mla":"Filakovský, Marek, et al. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs.” <i>41st International Symposium on Theoretical Aspects of Computer Science</i>, vol. 289, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2024.34\">10.4230/LIPIcs.STACS.2024.34</a>."},"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).","title":"Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs","date_updated":"2024-03-25T07:45:54Z","month":"03","scopus_import":"1","article_processing_charge":"No","quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"       289","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"oa":1,"file":[{"checksum":"0524d4189fd1ed08989546511343edf3","file_id":"15175","date_created":"2024-03-25T07:44:30Z","success":1,"relation":"main_file","access_level":"open_access","file_name":"2024_LIPICs_Filakovsky.pdf","date_updated":"2024-03-25T07:44:30Z","file_size":927290,"content_type":"application/pdf","creator":"dernst"}],"file_date_updated":"2024-03-25T07:44:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"41st International Symposium on Theoretical Aspects of Computer Science","day":"01","publication_status":"published","date_published":"2024-03-01T00:00:00Z","conference":{"name":"STACS: Symposium on Theoretical Aspects of Computer Science","start_date":"2024-03-12","end_date":"2024-03-14","location":"Clermont-Ferrand, France"},"volume":289,"alternative_title":["LIPIcs"],"_id":"15168","doi":"10.4230/LIPIcs.STACS.2024.34","author":[{"first_name":"Marek","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","last_name":"Filakovský","full_name":"Filakovský, Marek"},{"full_name":"Nakajima, Tamio Vesa","last_name":"Nakajima","first_name":"Tamio Vesa"},{"id":"ec596741-c539-11ec-b829-c79322a91242","orcid":"0000-0003-1245-3456","full_name":"Opršal, Jakub","last_name":"Opršal","first_name":"Jakub"},{"first_name":"Gianluca","id":"0433290C-AF8F-11E9-A4C7-F729E6697425","last_name":"Tasinato","full_name":"Tasinato, Gianluca"},{"full_name":"Wagner, Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli"}],"project":[{"grant_number":"P31312","call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425","name":"Algorithms for Embeddings and Homotopy Theory"},{"name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413"}],"external_id":{"arxiv":["2312.12981"]}}