{"id":"https://openalex.org/W3007271564","doi":"https://doi.org/10.1017/s0963548321000213","title":"Clustered 3-colouring graphs of bounded degree","display_name":"Clustered 3-colouring graphs of bounded degree","publication_year":2021,"publication_date":"2021-06-18","ids":{"openalex":"https://openalex.org/W3007271564","doi":"https://doi.org/10.1017/s0963548321000213","mag":"3007271564"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548321000213","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548321000213","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.11721","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000058655","display_name":"Vida Dujmovi\u0107","orcid":"https://orcid.org/0000-0001-7250-0600"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]},{"id":"https://openalex.org/I75381157","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05","country_code":"CA","type":"education","lineage":["https://openalex.org/I75381157"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vida Dujmovi\u0107","raw_affiliation_strings":["School of Computer Science and Electrical Engineering, University of Ottawa, Ottawa, Canada","University of Ottawa [Ottawa] (75 Laurier Avenue East, Ottawa, ON K1N 6N5 - Canada)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Electrical Engineering, University of Ottawa, Ottawa, Canada","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"University of Ottawa [Ottawa] (75 Laurier Avenue East, Ottawa, ON K1N 6N5 - Canada)","institution_ids":["https://openalex.org/I153718931","https://openalex.org/I75381157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038720048","display_name":"Louis Esperet","orcid":"https://orcid.org/0000-0001-6200-0514"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210094718","display_name":"Laboratoire des Sciences pour la Conception, l'Optimisation et la Production","ror":"https://ror.org/00rv5x925","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210094718","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Louis Esperet","raw_affiliation_strings":["Laboratoire G-SCOP (CNRS, Univ. Grenoble Alpes), Grenoble, France","G-SCOP_OC - Optimisation Combinatoire (46 Avenue F\u00e9lix Viallet 38001 GRENOBLE Cedex 1 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire G-SCOP (CNRS, Univ. Grenoble Alpes), Grenoble, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210094718","https://openalex.org/I899635006"]},{"raw_affiliation_string":"G-SCOP_OC - Optimisation Combinatoire (46 Avenue F\u00e9lix Viallet 38001 GRENOBLE Cedex 1 - France)","institution_ids":["https://openalex.org/I4210094718"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045902784","display_name":"Pat Morin","orcid":"https://orcid.org/0000-0003-0471-4118"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pat Morin","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada","Carleton University (1125 Colonel By Drive Ottawa, ON, Canada - Canada)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]},{"raw_affiliation_string":"Carleton University (1125 Colonel By Drive Ottawa, ON, Canada - Canada)","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088609870","display_name":"Bartosz Walczak","orcid":"https://orcid.org/0000-0002-5761-2564"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Bartosz Walczak","raw_affiliation_strings":["Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","UJ - Uniwersytet Jagiello\u0144ski w Krakowie = Jagiellonian University (ul. Go\u0142\u0119bia 24, 31-007 Krak\u00f3w - Poland)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"UJ - Uniwersytet Jagiello\u0144ski w Krakowie = Jagiellonian University (ul. Go\u0142\u0119bia 24, 31-007 Krak\u00f3w - Poland)","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066302647","display_name":"David R. Wood","orcid":"https://orcid.org/0000-0001-8866-3041"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"David R. Wood","raw_affiliation_strings":["School of Mathematics, Monash University, Melbourne, Australia","Monash University [Melbourne] (Victoria 3800, Australia  - Australia)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Monash University, Melbourne, Australia","institution_ids":["https://openalex.org/I56590836"]},{"raw_affiliation_string":"Monash University [Melbourne] (Victoria 3800, Australia  - Australia)","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5066302647"],"corresponding_institution_ids":["https://openalex.org/I56590836"],"apc_list":null,"apc_paid":null,"fwci":1.8498,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.86653142,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"31","issue":"1","first_page":"123","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8262782692909241},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6965349316596985},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6845530271530151},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6546235084533691},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6039738059043884},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5585945844650269},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.542419970035553},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48854121565818787},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4467836916446686},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3755805492401123},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.31748682260513306},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06800693273544312},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06675946712493896}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8262782692909241},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6965349316596985},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6845530271530151},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6546235084533691},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6039738059043884},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5585945844650269},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.542419970035553},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48854121565818787},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4467836916446686},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3755805492401123},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.31748682260513306},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06800693273544312},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06675946712493896},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548321000213","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548321000213","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.11721","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.11721","pdf_url":"https://arxiv.org/pdf/2002.11721","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ruj.uj.edu.pl:item/288601","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/288601","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"},{"id":"pmh:oai:HAL:hal-02975327v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02975327","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability and Computing, 2022, 31 (1), pp.123-135. ⟨10.1017/S0963548321000213⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.11721","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.11721","pdf_url":"https://arxiv.org/pdf/2002.11721","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1199503345","display_name":"Graph Reconfiguration","funder_award_id":"ANR-18-CE40-0032","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8181396905","display_name":"Graphs, Algorithms and TOpology","funder_award_id":"ANR-16-CE40-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":75,"referenced_works":["https://openalex.org/W132145278","https://openalex.org/W594463866","https://openalex.org/W1597094575","https://openalex.org/W1666845907","https://openalex.org/W1822246743","https://openalex.org/W1936855748","https://openalex.org/W1966682191","https://openalex.org/W1973474784","https://openalex.org/W1981254886","https://openalex.org/W1986861105","https://openalex.org/W1987286551","https://openalex.org/W2002722727","https://openalex.org/W2008440715","https://openalex.org/W2029448190","https://openalex.org/W2032560040","https://openalex.org/W2035409201","https://openalex.org/W2038643780","https://openalex.org/W2067431706","https://openalex.org/W2073734137","https://openalex.org/W2087083200","https://openalex.org/W2109001973","https://openalex.org/W2111027810","https://openalex.org/W2128660769","https://openalex.org/W2131433460","https://openalex.org/W2145062394","https://openalex.org/W2148360835","https://openalex.org/W2156760067","https://openalex.org/W2158540447","https://openalex.org/W2172244659","https://openalex.org/W2293551253","https://openalex.org/W2294414813","https://openalex.org/W2345501529","https://openalex.org/W2519651985","https://openalex.org/W2564849958","https://openalex.org/W2743168372","https://openalex.org/W2763761526","https://openalex.org/W2766116208","https://openalex.org/W2796847417","https://openalex.org/W2887773522","https://openalex.org/W2897886958","https://openalex.org/W2939652507","https://openalex.org/W2944976672","https://openalex.org/W2945078344","https://openalex.org/W2953295957","https://openalex.org/W2958387550","https://openalex.org/W2963041295","https://openalex.org/W2963368860","https://openalex.org/W2963446304","https://openalex.org/W2963838695","https://openalex.org/W2967815668","https://openalex.org/W2969015717","https://openalex.org/W2981502292","https://openalex.org/W3001673916","https://openalex.org/W3009498706","https://openalex.org/W3014452398","https://openalex.org/W3092025494","https://openalex.org/W3098333129","https://openalex.org/W3099033428","https://openalex.org/W3100878755","https://openalex.org/W3102574461","https://openalex.org/W3103128284","https://openalex.org/W3103189813","https://openalex.org/W3103394879","https://openalex.org/W3103615163","https://openalex.org/W3104062130","https://openalex.org/W3104982245","https://openalex.org/W3106391534","https://openalex.org/W3111722804","https://openalex.org/W3123414474","https://openalex.org/W3125642972","https://openalex.org/W3194359700","https://openalex.org/W4211173638","https://openalex.org/W4299736202","https://openalex.org/W4319589071","https://openalex.org/W6730763712"],"related_works":["https://openalex.org/W2045730620","https://openalex.org/W2395770054","https://openalex.org/W603403972","https://openalex.org/W2949729914","https://openalex.org/W2168266982","https://openalex.org/W2963028755","https://openalex.org/W4226287252","https://openalex.org/W2133160845","https://openalex.org/W2374423782","https://openalex.org/W2101009118"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"(not":[2],"necessarily":[3],"proper)":[4],"vertex":[5],"colouring":[6],"of":[7,59,67],"a":[8,57,64,82],"graph":[9],"has":[10,17],"clustering":[11,34,88],"c":[12,20],"if":[13],"every":[14],"monochromatic":[15],"component":[16],"at":[18],"most":[19],"vertices.":[21],"We":[22,71],"prove":[23,73],"that":[24,52,74,80],"planar":[25,47],"graphs":[26,48,51,75],"with":[27,33,63,76,87],"maximum":[28,77],"degree":[29,78],"$\\Delta$":[30,79,101],"are":[31,85],"3-colourable":[32,86],"$O(\\Delta^2)$":[35],".":[36,43,90,102],"The":[37,91],"previous":[38,93],"best":[39,92],"bound":[40,94],"was":[41,98],"$O(\\Delta^{37})$":[42],"This":[44],"result":[45,97],"for":[46,95],"generalises":[49],"to":[50],"can":[53],"be":[54],"drawn":[55],"on":[56],"surface":[58],"bounded":[60,65],"Euler":[61],"genus":[62],"number":[66],"crossings":[68],"per":[69],"edge.":[70],"then":[72],"exclude":[81],"fixed":[83],"minor":[84],"$O(\\Delta^5)$":[89],"this":[96],"exponential":[99],"in":[100]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2020-03-06T00:00:00"}