{"id":"https://openalex.org/W2161997644","doi":"https://doi.org/10.1002/jgt.3190150306","title":"[<i>a,b</i>]\u2010factorizations of graphs","display_name":"[<i>a,b</i>]\u2010factorizations of graphs","publication_year":1991,"publication_date":"1991-07-01","ids":{"openalex":"https://openalex.org/W2161997644","doi":"https://doi.org/10.1002/jgt.3190150306","mag":"2161997644"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190150306","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190150306","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/A5102140498","display_name":"Mao-cheng Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cai Mao\u2010Cheng","raw_affiliation_strings":["Institute of Systems Science Academia Sinica, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Systems Science Academia Sinica, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102140498"],"corresponding_institution_ids":["https://openalex.org/I4210120485"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.24346373,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"3","first_page":"283","last_page":"301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9970999956130981,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9958999752998352,"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":0.8602436184883118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7183308601379395},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.656940758228302},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5536688566207886},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4134542644023895}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8602436184883118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7183308601379395},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.656940758228302},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5536688566207886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4134542644023895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190150306","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190150306","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":[{"id":"https://openalex.org/F4320321041","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784"},{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1975558042","https://openalex.org/W2011164326","https://openalex.org/W2018140157","https://openalex.org/W2039779720","https://openalex.org/W2048484904","https://openalex.org/W2066743906","https://openalex.org/W2335389215","https://openalex.org/W3147498869","https://openalex.org/W3192960030","https://openalex.org/W4254106274","https://openalex.org/W4256646394"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"a":[2,10,23,47,51,94,98,116,127,131,148,158,162,180],"and":[3,41,152,187,201,206],"b":[4,8,31,91,106,119,124,139,150,155,170,182],"be":[5,69],"integers":[6],"with":[7],"\u2a7e":[9,11],"0.":[12],"A":[13,59],"graph":[14,48,60],"G":[15,26,39,49,57],"is":[16,50,61,80,114,146,178],"called":[17],"an":[18,42,104,136,167],"[":[19,43,53,62,72,195],"a,b":[20,44,54,63,73,196],"]\u2010graph":[21,113,145,177],"if":[22,65,88,123,154],"\u2a7d":[24,30,90,92,125,156],"d":[25],"(":[27,38],"v":[28,35],")":[29],"for":[32],"each":[33],"vertex":[34],"\u2208":[36],"V":[37],"),":[40],"]\u2010factor":[45],"of":[46,56,77,199],"spanning":[52],"]\u2010subgraph":[55],".":[58],"]\u2010factorable":[64],"its":[66],"edges":[67],"can":[68],"decomposed":[70],"into":[71],"]\u2010factors.":[74],"The":[75],"purpose":[76],"this":[78],"paper":[79],"to":[81],"prove":[82],"the":[83],"following":[84],"three":[85],"theorems:":[86],"(i)":[87],"1":[89],"2":[93,103,111,118,126,135,143,157,166,175],",":[95,117,137,168],"every":[96,129,160],"[(12":[97,130],"+":[99,102,107,110,120,134,142,165,171,174,183],"2)":[100,172],"m":[101,109,133,141,164,173,186],",(12":[105],"4)":[108],"bn":[112,144,176],"[2":[115,147,179],"1]\u2010factorable;":[121],"(ii)":[122],"\u22121,":[128,159],"\u22124)":[132],"(12":[138],"\u22122)":[140,163],"\u22121,2":[149,181],"]\u2010factorable;":[151],"(iii)":[153],"[(6":[161],"(6":[169],"1]\u2010factorable,":[184],"where":[185],"n":[188],"are":[189],"nonnegative":[190],"integers.":[191],"They":[192],"generalize":[193],"some":[194],"]\u2010factorization":[197],"results":[198],"Akiyama":[200],"Kano":[202,204],"[3],":[203],"[6],":[205],"Era":[207],"[5].":[208]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
