{"id":"https://openalex.org/W2119549171","doi":"https://doi.org/10.1017/s0963548302005485","title":"Equitable Colourings of <i>d</i>-degenerate Graphs","display_name":"Equitable Colourings of <i>d</i>-degenerate Graphs","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2119549171","doi":"https://doi.org/10.1017/s0963548302005485","mag":"2119549171"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548302005485","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005485","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080894223","display_name":"Alexandr Kostochka","orcid":"https://orcid.org/0000-0002-6363-3804"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU","US"],"is_corresponding":true,"raw_author_name":"A. V. KOSTOCHKA","raw_affiliation_strings":["Institute of Mathematics, Novosibirsk, Russia 630090","University of Illinois, Urbana, IL 61801, USA"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Novosibirsk, Russia 630090","institution_ids":["https://openalex.org/I4210096862"]},{"raw_affiliation_string":"University of Illinois, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023616108","display_name":"Kittikorn Nakprasit","orcid":"https://orcid.org/0000-0002-0421-3631"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"K. NAKPRASIT","raw_affiliation_strings":["Institute of Mathematics, Novosibirsk, Russia 630090"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Novosibirsk, Russia 630090","institution_ids":["https://openalex.org/I4210096862"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080894223"],"corresponding_institution_ids":["https://openalex.org/I157725225","https://openalex.org/I4210096862"],"apc_list":null,"apc_paid":null,"fwci":0.3545,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.62401884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"12","issue":"1","first_page":"53","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9847000241279602,"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":0.9847000241279602,"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":0.9478999972343445,"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":0.8094394207000732},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.763353168964386},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6524998545646667},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6478242874145508},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6126960515975952},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.45730382204055786},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3840150237083435},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1643344759941101}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8094394207000732},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.763353168964386},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6524998545646667},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6478242874145508},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6126960515975952},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.45730382204055786},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3840150237083435},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1643344759941101},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548302005485","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005485","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:CiteSeerX.psu:10.1.1.225.2941","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.225.2941","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/%7Ekostochk/docs/2004/cpc03n.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1479863711","https://openalex.org/W1964923438","https://openalex.org/W1971010556","https://openalex.org/W2041206070","https://openalex.org/W2156856270","https://openalex.org/W2167318613"],"related_works":["https://openalex.org/W2353039109","https://openalex.org/W4315588385","https://openalex.org/W3124638673","https://openalex.org/W2066153363","https://openalex.org/W2900100504","https://openalex.org/W2061564118","https://openalex.org/W4318566977","https://openalex.org/W4254898719","https://openalex.org/W2146196898","https://openalex.org/W42028307"],"abstract_inverted_index":{"A":[0],"proper":[1],"vertex":[2],"coloring":[3],"of":[4,13],"a":[5],"graph":[6,35],"is":[7],"called":[8],"equitable":[9,44],"if":[10],"the":[11,26],"sizes":[12],"colour":[14],"classes":[15],"differ":[16],"by":[17],"at":[18,39],"most":[19,40],"1.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24],"find":[25],"minimum":[27],"number":[28],"l=l(d,":[29],"\u0394)":[30],"such":[31],"that":[32],"every":[33,47],"d-degenerate":[34],"with":[36],"maximum":[37],"degree":[38],"\u0394":[41],"admits":[42],"an":[43],"t-colouring":[45],"for":[46],"t[ges":[48],"]l":[49],"when":[50],"\u0394[ges":[51],"]27d.":[52]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
