{"id":"https://openalex.org/W1975558042","doi":"https://doi.org/10.1002/jgt.3190090110","title":"Almost\u2010regular factorization of graphs","display_name":"Almost\u2010regular factorization of graphs","publication_year":1985,"publication_date":"1985-03-01","ids":{"openalex":"https://openalex.org/W1975558042","doi":"https://doi.org/10.1002/jgt.3190090110","mag":"1975558042"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190090110","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190090110","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5005795132","display_name":"Jin Akiyama","orcid":"https://orcid.org/0000-0002-0047-6717"},"institutions":[{"id":"https://openalex.org/I1314466530","display_name":"Tokai University","ror":"https://ror.org/01p7qe739","country_code":"JP","type":"education","lineage":["https://openalex.org/I1314466530"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jin Akiyama","raw_affiliation_strings":["Tokai University Hiratsuka, 259-12, Japan","Tokai University, Hiratsuka 259-12, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokai University Hiratsuka, 259-12, Japan","institution_ids":["https://openalex.org/I1314466530"]},{"raw_affiliation_string":"Tokai University, Hiratsuka 259-12, Japan","institution_ids":["https://openalex.org/I1314466530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062422841","display_name":"Mikio Kan\u014d","orcid":"https://orcid.org/0000-0002-7545-0327"},"institutions":[{"id":"https://openalex.org/I4210117807","display_name":"National Institute of Technology, Akashi College","ror":"https://ror.org/029kvcs29","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210117807","https://openalex.org/I4210120810"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mikio Kano","raw_affiliation_strings":["Akashi Technological College Akashi, 674, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Akashi Technological College Akashi, 674, Japan","institution_ids":["https://openalex.org/I4210117807"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.5497,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.64369237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"9","issue":"1","first_page":"123","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13991","display_name":"Nuclear Receptors and Signaling","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/combinatorics","display_name":"Combinatorics","score":0.8877721428871155},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8365949392318726},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.7273315191268921},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6028217077255249},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5962166786193848},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4163249731063843}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8877721428871155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8365949392318726},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.7273315191268921},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6028217077255249},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5962166786193848},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4163249731063843}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190090110","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190090110","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1767780339","https://openalex.org/W2039779720","https://openalex.org/W2066743906","https://openalex.org/W2133657109","https://openalex.org/W2335389215","https://openalex.org/W2495758475","https://openalex.org/W2799004609","https://openalex.org/W3192960030","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W2376029318","https://openalex.org/W2388301251","https://openalex.org/W3013941779","https://openalex.org/W1998659141","https://openalex.org/W3195376785","https://openalex.org/W2370435933","https://openalex.org/W138938013","https://openalex.org/W2947625790","https://openalex.org/W1975877275","https://openalex.org/W4318719574"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"integers":[2,85],"a":[3,8,10,18,35,41,61,89,133],"and":[4,30,81,86,143],"b,":[5,12],"0":[6],"\u2a7d":[7,9,11,19,22,42,45],"an":[13,31],"[a,":[14,32,54,67,76],"b]\u2010graph":[15],"G":[16],"satisties":[17],"deg(x,":[20,43],"G)":[21],"b":[23,46,59],"for":[24,47],"every":[25,48,95,116],"vertex":[26,49],"x":[27,50],"of":[28,51,136],"G,":[29],"b]\u2010factor":[33,55],"is":[34,56,66,88,106,127,132],"spanning":[36],"subgraph":[37],"F":[38],"such":[39],"that":[40,94,115],"F)":[44],"F.":[52],"An":[53],"almost\u2010regular":[57],"if":[58,69],"=":[60],"+":[62,97,99,102,104,108,118,125,129],"1.":[63],"A":[64],"graph":[65],"b]\u2010factorable":[68],"its":[70,111],"edges":[71],"can":[72],"be":[73],"decomposed":[74],"into":[75],"b]\u2010factors.":[77],"When":[78],"both":[79],"K":[80],"t":[82],"are":[83],"positive":[84],"s":[87],"nonnegative":[90],"integer,":[91],"we":[92,113],"prove":[93,114],"[(12K":[96],"2)t":[98],"2ks,":[100],"(12k":[101],"4)t":[103],"2ks]\u2010graph":[105],"[2k,2k":[107],"1]\u2010factorable.":[109],"As":[110],"corollary,":[112],"[r.r":[117],"1]\u2010graph":[119],"with":[120],"r":[121],"\u2a7e":[122],"12k":[123],"2":[124],"2k":[126],"[2k":[128],"1]\u2010factorable,":[130],"which":[131],"partial":[134],"extension":[135],"the":[137,144],"two":[138],"results,":[139],"one":[140],"by":[141,146],"Thomassen":[142],"other":[145],"Era.":[147]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
