{"id":"https://openalex.org/W2099674692","doi":"https://doi.org/10.1142/s1793830912500425","title":"A QUESTION ON RELAXED EQUITABLE COLORING","display_name":"A QUESTION ON RELAXED EQUITABLE COLORING","publication_year":2012,"publication_date":"2012-08-06","ids":{"openalex":"https://openalex.org/W2099674692","doi":"https://doi.org/10.1142/s1793830912500425","mag":"2099674692"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500425","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500425","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5053672565","display_name":"Wei Gao","orcid":"https://orcid.org/0000-0001-7963-3502"},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"WEI GAO","raw_affiliation_strings":["Department of Mathematics, Soochow University, Jiangsu Suzhou 215006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Soochow University, Jiangsu Suzhou 215006, China","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039774871","display_name":"Fen Zhou","orcid":"https://orcid.org/0000-0002-6090-6600"},"institutions":[{"id":"https://openalex.org/I4210086486","display_name":"Zhaotong University","ror":"https://ror.org/00264zf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210086486"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"FEN ZHOU","raw_affiliation_strings":["Department of Computer Science, Zhaotong Teachers' College, Yunnan Zhaotong 657000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Zhaotong Teachers' College, Yunnan Zhaotong 657000, China","institution_ids":["https://openalex.org/I4210086486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3473,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64286699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"04","issue":"03","first_page":"1250042","last_page":"1250042"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9909999966621399,"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":0.9909999966621399,"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":0.9876999855041504,"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":0.9606999754905701,"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/edge-coloring","display_name":"Edge coloring","score":0.7568035125732422},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7536731362342834},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.74405837059021},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.6347144842147827},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6200767159461975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5962241888046265},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.5267616510391235},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.5133141875267029},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.43570151925086975},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.42899924516677856},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39593085646629333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20178678631782532},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.14568710327148438},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.05767586827278137},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04946821928024292}],"concepts":[{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.7568035125732422},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7536731362342834},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.74405837059021},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.6347144842147827},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6200767159461975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5962241888046265},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.5267616510391235},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.5133141875267029},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.43570151925086975},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.42899924516677856},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39593085646629333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20178678631782532},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.14568710327148438},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.05767586827278137},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04946821928024292}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830912500425","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500425","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W658849301","https://openalex.org/W2001714541","https://openalex.org/W2009827511","https://openalex.org/W2011835719","https://openalex.org/W2043085939","https://openalex.org/W2101846098","https://openalex.org/W2102797028","https://openalex.org/W4232896595"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W4297911588","https://openalex.org/W3169197204","https://openalex.org/W2380525562","https://openalex.org/W4229747356","https://openalex.org/W1542397451","https://openalex.org/W398688634","https://openalex.org/W2585997002","https://openalex.org/W4320918672","https://openalex.org/W4252904121"],"abstract_inverted_index":{"An":[0],"equitable":[1,48],"(k,":[2,6],"d)-coloring":[3,7],"is":[4,9,22],"a":[5,17,23,46],"that":[8,19,26,59],"also":[10],"equitable.":[11],"In":[12],"this":[13],"paper,":[14],"we":[15],"raise":[16],"conjecture":[18],"if":[20,60],"G":[21,44,62],"graph":[24,61],"such":[25],"for":[27,69],"each":[28],"edge":[29,71],"xy":[30,72],"\u2208":[31,73],"E(G),":[32],"the":[33],"sum":[34],"d(x)":[35,64],"+":[36,41,52,65],"d(y)":[37,66],"at":[38],"most":[39],"2r":[40,68],"1,":[42],"then":[43,79],"has":[45],"d-relaxed":[47],"coloring":[49],"with":[50],"r":[51],"1":[53],"-":[54],"d":[55],"colors.":[56],"We":[57],"prove":[58],"meet":[63],"\u2264":[67],"every":[70],"E(G)":[74],"and":[75],"|G|":[76],"=":[77],"rs,":[78],"[Formula:":[80],"see":[81],"text].":[82]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
