{"id":"https://openalex.org/W4309189441","doi":"https://doi.org/10.1142/s1793830922501683","title":"Equitable critical graphs","display_name":"Equitable critical graphs","publication_year":2022,"publication_date":"2022-11-15","ids":{"openalex":"https://openalex.org/W4309189441","doi":"https://doi.org/10.1142/s1793830922501683"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922501683","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501683","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/A5014991891","display_name":"Loura Jency","orcid":"https://orcid.org/0000-0002-3840-2174"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Loura Jency","raw_affiliation_strings":["PG and Research Department of Mathematics, Loyola College, Chennai 600 034, India"],"raw_orcid":"https://orcid.org/0000-0002-3840-2174","affiliations":[{"raw_affiliation_string":"PG and Research Department of Mathematics, Loyola College, Chennai 600 034, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016545902","display_name":"Benedict Michael Raj","orcid":null},"institutions":[{"id":"https://openalex.org/I4076070","display_name":"Bharathidasan University","ror":"https://ror.org/02w7vnb60","country_code":"IN","type":"education","lineage":["https://openalex.org/I4076070"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Benedict Michael Raj","raw_affiliation_strings":["PG and Research Department of Mathematics, St. Joseph\u2019s College (Affiliated to Bharathidasan University), Trichy 620 002, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PG and Research Department of Mathematics, St. Joseph\u2019s College (Affiliated to Bharathidasan University), Trichy 620 002, India","institution_ids":["https://openalex.org/I4076070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014991891"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16721812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"08","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":0.9987000226974487,"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":0.9987000226974487,"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":0.9854000210762024,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9674999713897705,"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/critical-graph","display_name":"Critical graph","score":0.6649417877197266},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6526966094970703},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5518541932106018},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5381231307983398},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5090036392211914},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5014581680297852},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40222564339637756},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.13976126909255981},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.075747549533844}],"concepts":[{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.6649417877197266},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6526966094970703},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5518541932106018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5381231307983398},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5090036392211914},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5014581680297852},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40222564339637756},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.13976126909255981},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.075747549533844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922501683","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501683","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":[{"id":"https://metadata.un.org/sdg/10","score":0.4300000071525574,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W658849301","https://openalex.org/W1495288901","https://openalex.org/W1973336897","https://openalex.org/W1991925535","https://openalex.org/W2029105623","https://openalex.org/W2058115709","https://openalex.org/W2090681852","https://openalex.org/W2136086442","https://openalex.org/W2171103562","https://openalex.org/W2522963175","https://openalex.org/W4229647732","https://openalex.org/W4249035553"],"related_works":["https://openalex.org/W2950817880","https://openalex.org/W2562183448","https://openalex.org/W1984098916","https://openalex.org/W2046610653","https://openalex.org/W2168180506","https://openalex.org/W2057367302","https://openalex.org/W2091414672","https://openalex.org/W2891101917","https://openalex.org/W2951887113","https://openalex.org/W3178681420"],"abstract_inverted_index":{"A":[0,76],"proper":[1,91],"vertex":[2,124,129],"coloring":[3],"of":[4,15,29,64,96],"a":[5,30],"graph":[6,31,77],"[Formula:":[7,32,37,43,48,53,72,78,86,93,97,100,106,113],"see":[8,33,38,44,49,54,73,79,87,94,98,101,107,114],"text]":[9,45,50,80,88,95,102],"is":[10,40,51,81,103,111],"equitable":[11,26,65,71,83,105,112,117,123,127],"if":[12,85,109],"the":[13,41],"sizes":[14],"any":[16],"two":[17],"color":[18],"classes":[19],"differ":[20],"by":[21,36],"at":[22],"most":[23],"one.":[24],"The":[25],"chromatic":[27],"number":[28],"text],":[34,39],"denoted":[35],"minimum":[42],"such":[46],"that":[47,122],"equitably":[52],"text]-colorable.":[55],"In":[56],"this":[57],"paper,":[58],"we":[59,120],"discuss":[60,121],"some":[61],"basic":[62],"properties":[63],"critical":[66,84,128],"graphs":[67],"as":[68,70],"well":[69],"text]-critical":[74,108],"graphs.":[75,131],"called":[82,104],"for":[89],"every":[90],"subgraph":[92],"text].":[99],"it":[110],"text]-chromatic":[115],"and":[116],"critical.":[118],"Furthermore,":[119],"(edge)":[125,130],"critical,":[126]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
