{"id":"https://openalex.org/W4298110741","doi":"https://doi.org/10.1017/s0963548322000268","title":"Improved bound for improper colourings of graphs with no odd clique minor","display_name":"Improved bound for improper colourings of graphs with no odd clique minor","publication_year":2022,"publication_date":"2022-09-30","ids":{"openalex":"https://openalex.org/W4298110741","doi":"https://doi.org/10.1017/s0963548322000268"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548322000268","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548322000268","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1379954D4625F660F6C935A2B6DFB72/S0963548322000268a.pdf/div-class-title-improved-bound-for-improper-colourings-of-graphs-with-no-odd-clique-minor-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1379954D4625F660F6C935A2B6DFB72/S0963548322000268a.pdf/div-class-title-improved-bound-for-improper-colourings-of-graphs-with-no-odd-clique-minor-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048260458","display_name":"Raphael Steiner","orcid":"https://orcid.org/0000-0002-4234-6136"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Raphael Steiner","raw_affiliation_strings":["Department of Computer Science, Institute of Theoretical Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-4234-6136","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Institute of Theoretical Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048260458"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.2874,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58507195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"32","issue":"2","first_page":"326","last_page":"333"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.982699990272522,"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":0.868407130241394},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.8049031496047974},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7364644408226013},{"id":"https://openalex.org/keywords/clique-number","display_name":"Clique number","score":0.7027948498725891},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6921358108520508},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5526446104049683},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.5410867929458618},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5312670469284058},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4813419282436371},{"id":"https://openalex.org/keywords/graph-minor","display_name":"Graph minor","score":0.47504711151123047},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3834573030471802},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.18224847316741943},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1530837118625641},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.10162052512168884}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.868407130241394},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.8049031496047974},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7364644408226013},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.7027948498725891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6921358108520508},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5526446104049683},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.5410867929458618},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5312670469284058},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4813419282436371},{"id":"https://openalex.org/C140752511","wikidata":"https://www.wikidata.org/wiki/Q905837","display_name":"Graph minor","level":5,"score":0.47504711151123047},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3834573030471802},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.18224847316741943},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1530837118625641},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.10162052512168884},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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":3,"locations":[{"id":"doi:10.1017/s0963548322000268","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548322000268","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1379954D4625F660F6C935A2B6DFB72/S0963548322000268a.pdf/div-class-title-improved-bound-for-improper-colourings-of-graphs-with-no-odd-clique-minor-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:research-collection.ethz.ch:20.500.11850/575916","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/575916","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability & Computing, 32 (2)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.3929/ethz-b-000575916","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000575916","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1017/s0963548322000268","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548322000268","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D1379954D4625F660F6C935A2B6DFB72/S0963548322000268a.pdf/div-class-title-improved-bound-for-improper-colourings-of-graphs-with-no-odd-clique-minor-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321652","display_name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","ror":"https://ror.org/05a28rw58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4298110741.pdf","grobid_xml":"https://content.openalex.org/works/W4298110741.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1520619927","https://openalex.org/W1572447597","https://openalex.org/W2027399467","https://openalex.org/W2034842587","https://openalex.org/W2039013898","https://openalex.org/W2047936368","https://openalex.org/W2047993669","https://openalex.org/W2049053276","https://openalex.org/W2059021689","https://openalex.org/W2109001973","https://openalex.org/W2132677029","https://openalex.org/W2158540447","https://openalex.org/W2170758948","https://openalex.org/W2476848496","https://openalex.org/W2504259738","https://openalex.org/W2564849958","https://openalex.org/W2953295957","https://openalex.org/W2963041295","https://openalex.org/W3018833318","https://openalex.org/W3098333129","https://openalex.org/W3102574461","https://openalex.org/W3125642972","https://openalex.org/W3198262761","https://openalex.org/W3198820907","https://openalex.org/W6749512965","https://openalex.org/W6771700640","https://openalex.org/W6776056834"],"related_works":["https://openalex.org/W83147424","https://openalex.org/W2152982698","https://openalex.org/W2563767922","https://openalex.org/W2968633427","https://openalex.org/W300955832","https://openalex.org/W4299693959","https://openalex.org/W2952707850","https://openalex.org/W2275773863","https://openalex.org/W3026920247","https://openalex.org/W2950983641"],"abstract_inverted_index":{"Abstract":[0],"Strengthening":[1],"Hadwiger\u2019s":[2,28],"conjecture,":[3,38],"Gerards":[4],"and":[5,100,109,115,123,188,200],"Seymour":[6],"conjectured":[7],"in":[8,157,168],"1995":[9],"that":[10,42,56,134,144],"every":[11,43],"graph":[12,44,146,182],"with":[13,45,206],"no":[14,46],"odd":[15,47,215],"$K_t$":[16,48,148,203,216],"-minor":[17,49],"is":[18,23,75,147,160],"properly":[19],"$(t-1)$":[20],"-colourable.":[21],"This":[22],"known":[24],"as":[25],"the":[26,36,71,88,135,140,145,152,155,170,181,194,212],"Odd":[27],"conjecture":[29],".":[30,67],"We":[31],"prove":[32],"a":[33,51,79,117,177],"relaxation":[34],"of":[35,73,81,165,186],"above":[37,136],"namely":[39],"we":[40],"show":[41],"admits":[50],"vertex":[52],"$(2t-2)$":[53],"-colouring":[54],"such":[55],"all":[57],"monochromatic":[58],"components":[59],"have":[60],"size":[61],"at":[62],"most":[63],"$\\lceil":[64],"\\frac{1}{2}(t-2)":[65],"\\rceil$":[66],"The":[68],"bound":[69,153],"on":[70,154,172],"number":[72],"colours":[74],"optimal":[76],"up":[77],"to":[78,214],"factor":[80],"$2$":[82],",":[83],"improves":[84],"previous":[85,166],"bounds":[86],"for":[87,202],"same":[89],"problem":[90],"by":[91,119,176,196],"Kawarabayashi":[92],"(2008,":[93],"Combin.":[94,103],"Probab.":[95,104],"Comput.":[96,105],"17":[97],"815\u2013821),":[98],"Kang":[99],"Oum":[101],"(2019,":[102],"28":[106],"740\u2013754),":[107],"Liu":[108],"Wood":[110,124,201],"(2021,":[111],"arXiv":[112],"preprint,":[113],"arXiv:1905.09495),":[114],"strengthens":[116],"result":[118,159],"van":[120,197],"den":[121,198],"Heuvel":[122,199],"(2018,":[125],"J.":[126],"Lond.":[127],"Math.":[128],"Soc.":[129],"98":[130],"129\u2013148),":[131],"who":[132],"showed":[133],"conclusion":[137],"holds":[138],"under":[139],"more":[141],"restrictive":[142],"assumption":[143],"-minor-free.":[149],"In":[150],"addition,":[151],"component-size":[156],"our":[158],"much":[161],"smaller":[162],"than":[163],"those":[164],"results,":[167],"which":[169,210],"dependency":[171],"$t$":[173],"was":[174],"given":[175],"function":[178],"arising":[179],"from":[180],"minor":[183],"structure":[184],"theorem":[185],"Robertson":[187],"Seymour.":[189],"Our":[190],"short":[191],"proof":[192],"combines":[193],"method":[195],"-minor-free":[204,217],"graphs":[205,218],"some":[207],"additional":[208],"ideas,":[209],"make":[211],"extension":[213],"possible.":[219]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}