{"id":"https://openalex.org/W2962862260","doi":"https://doi.org/10.37236/6042","title":"Chromatic Index, Treewidth and Maximum Degree","display_name":"Chromatic Index, Treewidth and Maximum Degree","publication_year":2018,"publication_date":"2018-05-11","ids":{"openalex":"https://openalex.org/W2962862260","doi":"https://doi.org/10.37236/6042","mag":"2962862260"},"language":"en","primary_location":{"id":"doi:10.37236/6042","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6042","pdf_url":null,"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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6042","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081417865","display_name":"Henning Bruhn","orcid":"https://orcid.org/0000-0003-0484-6815"},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Henning Bruhn","raw_affiliation_strings":["Universit\u00e4t Ulm"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Ulm","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053429379","display_name":"Laura Gellert","orcid":"https://orcid.org/0000-0001-9386-4657"},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Laura Gellert","raw_affiliation_strings":["Universit\u00e4t Ulm"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Ulm","institution_ids":["https://openalex.org/I196349391"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103264872","display_name":"Richard Lang","orcid":"https://orcid.org/0000-0002-7661-934X"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Richard Lang","raw_affiliation_strings":["University of Birmingham"],"affiliations":[{"raw_affiliation_string":"University of Birmingham","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081417865"],"corresponding_institution_ids":["https://openalex.org/I196349391"],"apc_list":null,"apc_paid":null,"fwci":0.2019,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58247136,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"2","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":1.0,"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":1.0,"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":0.9994999766349792,"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":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8799706697463989},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.878291130065918},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.8321450352668762},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7630940079689026},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6488659977912903},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5556188821792603},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.5254548788070679},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4571819305419922},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.42553552985191345},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.2078777253627777},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.08491450548171997},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.06586262583732605},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.03969660401344299}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8799706697463989},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.878291130065918},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.8321450352668762},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7630940079689026},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6488659977912903},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5556188821792603},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.5254548788070679},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4571819305419922},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.42553552985191345},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.2078777253627777},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.08491450548171997},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.06586262583732605},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.03969660401344299},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/6042","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6042","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.37236/6042","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6042","pdf_url":null,"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/G8514069245","display_name":null,"funder_award_id":"EP/P002420/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W617577063","https://openalex.org/W1869361267","https://openalex.org/W1988512244","https://openalex.org/W1995035986","https://openalex.org/W1995705069","https://openalex.org/W2010629352","https://openalex.org/W2026087461","https://openalex.org/W2081414924","https://openalex.org/W2087083200","https://openalex.org/W2102669784","https://openalex.org/W2142206280","https://openalex.org/W2144392803","https://openalex.org/W2151370292","https://openalex.org/W2798588639","https://openalex.org/W2988480584"],"related_works":["https://openalex.org/W2949617446","https://openalex.org/W4294299870","https://openalex.org/W2748664888","https://openalex.org/W1582492864","https://openalex.org/W35387897","https://openalex.org/W2591659253","https://openalex.org/W2745231626","https://openalex.org/W4299559467","https://openalex.org/W2144392803","https://openalex.org/W2963750404"],"abstract_inverted_index":{"We":[0,28],"conjecture":[1,22],"that":[2,31],"any":[3,32],"graph":[4,33],"$G$":[5,34],"with":[6,35],"treewidth":[7,36],"$k$":[8],"and":[9,39],"maximum":[10,40],"degree":[11,41],"$\\Delta(G)\\geq":[12],"k":[13],"+":[14],"\\sqrt{k}$":[15],"satisfies":[16,43],"$\\chi'(G)=\\Delta(G)$.":[17],"In":[18],"support":[19],"of":[20,49],"the":[21],"we":[23],"prove":[24],"its":[25],"fractional":[26],"version.":[27],"also":[29],"show":[30],"$k\\geq":[37],"4$":[38],"$2k-1$":[42],"$\\chi'(G)=\\Delta(G)$,":[44],"extending":[45],"an":[46],"old":[47],"result":[48],"Vizing.":[50]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
