{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"article_number":"34","has_accepted_license":"1","ddc":["510"],"publication_identifier":{"isbn":["9783959773119"],"eissn":["1868-8969"]},"article_processing_charge":"No","citation":{"ista":"Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. 2024. Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. 41st International Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical Aspects of Computer Science, LIPIcs, vol. 289, 34.","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>.","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>","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>","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>.","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.","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."},"title":"Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs","intvolume":"       289","scopus_import":"1","quality_controlled":"1","date_published":"2024-03-01T00:00:00Z","volume":289,"year":"2024","oa":1,"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"}],"day":"01","language":[{"iso":"eng"}],"author":[{"last_name":"Filakovský","first_name":"Marek","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","full_name":"Filakovský, Marek"},{"full_name":"Nakajima, Tamio Vesa","first_name":"Tamio Vesa","last_name":"Nakajima"},{"full_name":"Opršal, Jakub","id":"ec596741-c539-11ec-b829-c79322a91242","first_name":"Jakub","orcid":"0000-0003-1245-3456","last_name":"Opršal"},{"first_name":"Gianluca","last_name":"Tasinato","full_name":"Tasinato, Gianluca","id":"0433290C-AF8F-11E9-A4C7-F729E6697425"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568","first_name":"Uli"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-03-25T07:45:54Z","type":"conference","department":[{"_id":"UlWa"}],"doi":"10.4230/LIPIcs.STACS.2024.34","oa_version":"Published Version","project":[{"grant_number":"P31312","call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425","name":"Algorithms for Embeddings and Homotopy Theory"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"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).","ec_funded":1,"file_date_updated":"2024-03-25T07:44:30Z","file":[{"success":1,"date_updated":"2024-03-25T07:44:30Z","access_level":"open_access","creator":"dernst","file_size":927290,"date_created":"2024-03-25T07:44:30Z","file_name":"2024_LIPICs_Filakovsky.pdf","checksum":"0524d4189fd1ed08989546511343edf3","content_type":"application/pdf","file_id":"15175","relation":"main_file"}],"_id":"15168","conference":{"name":"STACS: Symposium on Theoretical Aspects of Computer Science","start_date":"2024-03-12","end_date":"2024-03-14","location":"Clermont-Ferrand, France"},"status":"public","external_id":{"arxiv":["2312.12981"]},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","alternative_title":["LIPIcs"],"date_created":"2024-03-24T23:00:59Z","month":"03","publication":"41st International Symposium on Theoretical Aspects of Computer Science"}