{"id":"https://openalex.org/W3044049558","doi":"https://doi.org/10.37236/9785","title":"Chromatic Polynomials of 2-Edge-Coloured Graphs","display_name":"Chromatic Polynomials of 2-Edge-Coloured Graphs","publication_year":2023,"publication_date":"2023-12-14","ids":{"openalex":"https://openalex.org/W3044049558","doi":"https://doi.org/10.37236/9785","mag":"3044049558"},"language":"en","primary_location":{"id":"doi:10.37236/9785","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9785","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p40/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":"article","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/v30i4p40/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015525363","display_name":"Iain Beaton","orcid":"https://orcid.org/0000-0002-5464-8166"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Iain Beaton","raw_affiliation_strings":["Department of Mathematics and Statistics, Dalhousie University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Dalhousie University","institution_ids":["https://openalex.org/I129902397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078903170","display_name":"Danielle Cox","orcid":"https://orcid.org/0000-0002-3432-0083"},"institutions":[{"id":"https://openalex.org/I179301192","display_name":"Mount Saint Vincent University","ror":"https://ror.org/03g3p3b82","country_code":"CA","type":"education","lineage":["https://openalex.org/I179301192"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Danielle Cox","raw_affiliation_strings":["Mathematics Department, Mount Saint Vincent University"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Mount Saint Vincent University","institution_ids":["https://openalex.org/I179301192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023425187","display_name":"Christopher Duffy","orcid":"https://orcid.org/0000-0003-1657-3172"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Christopher Duffy","raw_affiliation_strings":["University of Melbourne"],"affiliations":[{"raw_affiliation_string":"University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052561333","display_name":"Nicole Zolkavich","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nicole Zolkavich","raw_affiliation_strings":["Department of Mathematics and Statistics, McGill University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McGill University","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015525363"],"corresponding_institution_ids":["https://openalex.org/I129902397"],"apc_list":null,"apc_paid":null,"fwci":0.3932,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60742732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"30","issue":"4","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":0.996999979019165,"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":0.996999979019165,"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":0.993399977684021,"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":0.9901999831199646,"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/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.8990894556045532},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7050880789756775},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6747492551803589},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5258781909942627},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4773833155632019},{"id":"https://openalex.org/keywords/friendship-graph","display_name":"Friendship graph","score":0.4762863516807556},{"id":"https://openalex.org/keywords/windmill-graph","display_name":"Windmill graph","score":0.46733415126800537},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45207712054252625},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.4457726776599884},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.42373722791671753},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3980567753314972},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.32284343242645264},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16332444548606873},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.08781495690345764}],"concepts":[{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.8990894556045532},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7050880789756775},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6747492551803589},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5258781909942627},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4773833155632019},{"id":"https://openalex.org/C70488441","wikidata":"https://www.wikidata.org/wiki/Q5504427","display_name":"Friendship graph","level":5,"score":0.4762863516807556},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.46733415126800537},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45207712054252625},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.4457726776599884},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.42373722791671753},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3980567753314972},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.32284343242645264},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16332444548606873},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.08781495690345764}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/9785","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9785","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p40/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:2007.13710","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.13710","pdf_url":"https://arxiv.org/pdf/2007.13710","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":"text"},{"id":"doi:10.48550/arxiv.2007.13710","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.13710","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:10.37236/9785","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9785","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p40/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/G1597412403","display_name":null,"funder_award_id":"RGPIN-","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3033569629","display_name":null,"funder_award_id":"2017-04401","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3216283581","display_name":null,"funder_award_id":"RGPIN-201","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G4719048210","display_name":null,"funder_award_id":"RGPIN-2017","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6221715925","display_name":null,"funder_award_id":"RGPIN","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6617295658","display_name":null,"funder_award_id":"2019-04857","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8284766523","display_name":null,"funder_award_id":"(NSERC)","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G832689143","display_name":null,"funder_award_id":"RGPIN-2019","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3044049558.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1607127543","https://openalex.org/W1679590246","https://openalex.org/W1985423710","https://openalex.org/W2008263650","https://openalex.org/W2024299660","https://openalex.org/W2032968509","https://openalex.org/W2051774645","https://openalex.org/W2130504407","https://openalex.org/W2154567859","https://openalex.org/W2200162493","https://openalex.org/W2441249653","https://openalex.org/W2611093227","https://openalex.org/W2897168502","https://openalex.org/W2963649630","https://openalex.org/W3000612418","https://openalex.org/W3160192199","https://openalex.org/W6656512103","https://openalex.org/W6765885026"],"related_works":["https://openalex.org/W2092041285","https://openalex.org/W2358377247","https://openalex.org/W2897657622","https://openalex.org/W2028417235","https://openalex.org/W2355004170","https://openalex.org/W2359595284","https://openalex.org/W2045328757","https://openalex.org/W2332295289","https://openalex.org/W2378138801","https://openalex.org/W2954936823"],"abstract_inverted_index":{"Using":[0],"the":[1,15,28,37,41,57,61,64,68,75,78],"definition":[2,16],"of":[3,5,17,32,44,60,67,77,80,90],"colouring":[4],"$2$-edge-coloured":[6],"graphs":[7,50],"derived":[8],"from":[9],"2-edge-coloured":[10,21],"graph":[11,62],"homomorphism,":[12],"we":[13,73],"extend":[14],"chromatic":[18,42,58,65,88],"polynomial":[19,34,43,59,66],"to":[20],"graphs.":[22,91],"We":[23,47],"find":[24],"closed":[25],"forms":[26],"for":[27,40,55],"first":[29],"three":[30],"coefficients":[31],"this":[33,81],"that":[35,51],"generalize":[36],"known":[38],"results":[39],"a":[45,53],"graph.":[46],"classify":[48],"those":[49],"admit":[52],"2-edge-colouring":[54,69],"which":[56],"and":[63],"is":[70],"equal.":[71],"Finally,":[72],"examine":[74],"behaviour":[76],"roots":[79],"polynomial,":[82],"highlighting":[83],"behaviours":[84],"not":[85],"seen":[86],"in":[87],"polynomials":[89]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2020-07-29T00:00:00"}