{"id":"https://openalex.org/W1527728086","doi":"https://doi.org/10.37236/4938","title":"The Chromatic Number of a Signed Graph","display_name":"The Chromatic Number of a Signed Graph","publication_year":2016,"publication_date":"2016-01-22","ids":{"openalex":"https://openalex.org/W1527728086","doi":"https://doi.org/10.37236/4938","mag":"1527728086"},"language":"en","primary_location":{"id":"doi:10.37236/4938","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4938","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p14/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p14/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038322764","display_name":"Edita M\u00e1\u010dajov\u00e1","orcid":"https://orcid.org/0000-0001-5735-5513"},"institutions":[{"id":"https://openalex.org/I74788687","display_name":"Comenius University Bratislava","ror":"https://ror.org/0587ef340","country_code":"SK","type":"education","lineage":["https://openalex.org/I74788687"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"Edita M\u00e1\u010dajov\u00e1","raw_affiliation_strings":["Comenius University in Bratislava"],"affiliations":[{"raw_affiliation_string":"Comenius University in Bratislava","institution_ids":["https://openalex.org/I74788687"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014990290","display_name":"Andr\u00e9 Raspaud","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Raspaud","raw_affiliation_strings":["LaBRI Universit de Bordeaux 33405 Talence Cedex, France","Laboratoire Bordelais de Recherche en Informatique"],"affiliations":[{"raw_affiliation_string":"LaBRI Universit de Bordeaux 33405 Talence Cedex, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254"]},{"raw_affiliation_string":"Laboratoire Bordelais de Recherche en Informatique","institution_ids":["https://openalex.org/I4210142254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033117907","display_name":"Martin \u0160koviera","orcid":"https://orcid.org/0000-0002-2108-7518"},"institutions":[{"id":"https://openalex.org/I74788687","display_name":"Comenius University Bratislava","ror":"https://ror.org/0587ef340","country_code":"SK","type":"education","lineage":["https://openalex.org/I74788687"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Martin \u0160koviera","raw_affiliation_strings":["Comenius University in Bratislava"],"affiliations":[{"raw_affiliation_string":"Comenius University in Bratislava","institution_ids":["https://openalex.org/I74788687"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038322764"],"corresponding_institution_ids":["https://openalex.org/I74788687"],"apc_list":null,"apc_paid":null,"fwci":0.3594,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.64074139,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"23","issue":"1","first_page":null,"last_page":null},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9979000091552734,"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/T11476","display_name":"Graph theory and applications","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/signed-graph","display_name":"Signed graph","score":0.9297983646392822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.758267879486084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.693311333656311},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6257675886154175},{"id":"https://openalex.org/keywords/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.5374532341957092},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5243594646453857},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5219654440879822},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4841809570789337},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.42018991708755493}],"concepts":[{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.9297983646392822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.758267879486084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.693311333656311},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6257675886154175},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.5374532341957092},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5243594646453857},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5219654440879822},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4841809570789337},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42018991708755493},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/4938","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4938","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p14/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1412.6349","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.6349","pdf_url":"https://arxiv.org/pdf/1412.6349","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":null},{"id":"mag:1527728086","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1412.6349v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1412.6349","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1412.6349","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/4938","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4938","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p14/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2077798120","display_name":null,"funder_award_id":"ANR-10-IDEX-","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G227995047","display_name":null,"funder_award_id":"1/0474/15","funder_id":"https://openalex.org/F4320323641","funder_display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV"},{"id":"https://openalex.org/G235163672","display_name":null,"funder_award_id":"VEGA 1/0474/15","funder_id":"https://openalex.org/F4320323641","funder_display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV"},{"id":"https://openalex.org/G2667004339","display_name":null,"funder_award_id":"10-IDEX-03-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2668054044","display_name":null,"funder_award_id":"ANR-10-IDEX-03-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2929008799","display_name":null,"funder_award_id":"ANR_10_IDEX_03_02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G302629176","display_name":null,"funder_award_id":"NR-10-IDEX-03-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3086235511","display_name":null,"funder_award_id":"ANR-10-IDEX-03-0","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3238091341","display_name":null,"funder_award_id":"ANR-10-IDEX-03-02)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G471331628","display_name":null,"funder_award_id":"ANR-10-IDEX","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7240651115","display_name":null,"funder_award_id":"ANR-10","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"},{"id":"https://openalex.org/F4320323641","display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","ror":"https://ror.org/044gwpv05"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1527728086.pdf","grobid_xml":"https://content.openalex.org/works/W1527728086.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W141699115","https://openalex.org/W1579049696","https://openalex.org/W1581277026","https://openalex.org/W1972168259","https://openalex.org/W1980769375","https://openalex.org/W1987745187","https://openalex.org/W2067698531","https://openalex.org/W2076679259","https://openalex.org/W2085716675","https://openalex.org/W2092825420"],"related_works":["https://openalex.org/W2963764468","https://openalex.org/W3173806834","https://openalex.org/W3184655893","https://openalex.org/W3169919287","https://openalex.org/W2964254008","https://openalex.org/W3031432612","https://openalex.org/W3084886684","https://openalex.org/W2997928242","https://openalex.org/W2949659588","https://openalex.org/W2130223805","https://openalex.org/W2891510334","https://openalex.org/W2883181337","https://openalex.org/W2963488730","https://openalex.org/W2095413237","https://openalex.org/W2077368329","https://openalex.org/W3003166427","https://openalex.org/W2000726024","https://openalex.org/W1916421046","https://openalex.org/W2025034352","https://openalex.org/W1599741884"],"abstract_inverted_index":{"In":[0],"1982,":[1],"Zaslavsky":[2],"introduced":[3],"the":[4,32,38,45,48,69,79,87,102,111,122,126,131,143],"concept":[5],"of":[6,11,47,54,71,73,81,89,101,105,114,121,125,134,142],"a":[7,12,17,90,98],"proper":[8],"vertex":[9],"colouring":[10],"signed":[13,63,75,82,94,135,148],"graph":[14,64,83],"$G$":[15],"as":[16],"mapping":[18],"$\\phi\\colon":[19],"V(G)\\to":[20],"\\mathbb{Z}$":[21],"such":[22],"that":[23],"for":[24,93],"any":[25],"two":[26],"adjacent":[27],"vertices":[28],"$u$":[29],"and":[30,138],"$v$":[31],"colour":[33,39],"$\\phi(u)$":[34],"is":[35,42,44],"different":[36],"from":[37],"$\\sigma(uv)\\phi(v)$,":[40],"where":[41],"$\\sigma(uv)$":[43],"sign":[46],"edge":[49],"$uv$.":[50],"The":[51],"substantial":[52],"part":[53],"Zaslavsky's":[55],"research":[56],"concentrated":[57],"on":[58,68],"polynomial":[59],"invariants":[60],"related":[61],"to":[62,147],"colourings":[65,72,84],"rather":[66],"than":[67],"behaviour":[70],"individual":[74],"graphs.":[76,149],"We":[77,109],"continue":[78],"study":[80],"by":[85],"proposing":[86],"definition":[88],"chromatic":[91,103,123,132],"number":[92,104,124,133],"graphs":[95],"which":[96],"provides":[97],"natural":[99],"extension":[100,141],"an":[106,140],"unsigned":[107,128],"graph.":[108],"establish":[110],"basic":[112],"properties":[113],"this":[115],"invariant,":[116],"provide":[117],"bounds":[118],"in":[119],"terms":[120],"underlying":[127],"graph,":[129],"investigate":[130],"planar":[136],"graphs,":[137],"prove":[139],"celebrated":[144],"Brooks'":[145],"theorem":[146]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}