{"id":"https://openalex.org/W4413228930","doi":"https://doi.org/10.1017/s0963548325100138","title":"A stability theorem for multi-partite graphs","display_name":"A stability theorem for multi-partite graphs","publication_year":2025,"publication_date":"2025-08-11","ids":{"openalex":"https://openalex.org/W4413228930","doi":"https://doi.org/10.1017/s0963548325100138"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548325100138","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548325100138","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/A5087581435","display_name":"Wanfang Chen","orcid":"https://orcid.org/0000-0003-1792-2370"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wanfang Chen","raw_affiliation_strings":["East China Normal University","School of Mathematical Sciences Key Laboratory of MEA(Ministry of Education) Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China Normal University","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"School of Mathematical Sciences Key Laboratory of MEA(Ministry of Education) Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100511661","display_name":"Changhong Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changhong Lu","raw_affiliation_strings":["East China Normal University","School of Mathematical Sciences Key Laboratory of MEA(Ministry of Education) Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China Normal University","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"School of Mathematical Sciences Key Laboratory of MEA(Ministry of Education) Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026657022","display_name":"Long\u2010Tu Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Long-Tu Yuan","raw_affiliation_strings":["East China Normal University","School of Mathematical Sciences Key Laboratory of MEA(Ministry of Education) Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"East China Normal University","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"School of Mathematical Sciences Key Laboratory of MEA(Ministry of Education) Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026657022"],"corresponding_institution_ids":["https://openalex.org/I66867065"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30332195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"6","first_page":"821","last_page":"847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"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/T11476","display_name":"Graph theory and applications","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9944999814033508,"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":0.7656099796295166},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7519168853759766},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"Extremal graph theory","score":0.629152238368988},{"id":"https://openalex.org/keywords/stability-theorem","display_name":"Stability theorem","score":0.6262469291687012},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5653315782546997},{"id":"https://openalex.org/keywords/intersection-theorem","display_name":"Intersection theorem","score":0.5489228367805481},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5404636859893799},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.5036277174949646},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.44847699999809265},{"id":"https://openalex.org/keywords/strong-perfect-graph-theorem","display_name":"Strong perfect graph theorem","score":0.4438631236553192},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4427146315574646},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.4358361065387726},{"id":"https://openalex.org/keywords/perfect-graph","display_name":"Perfect graph","score":0.4252889156341553},{"id":"https://openalex.org/keywords/robertson\u2013seymour-theorem","display_name":"Robertson\u2013Seymour theorem","score":0.42218613624572754},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4039068818092346},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.360828161239624},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.33414924144744873},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.31488752365112305},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.29785633087158203},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.26804929971694946},{"id":"https://openalex.org/keywords/danskins-theorem","display_name":"Danskin's theorem","score":0.2567480802536011},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.1803314983844757},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.06928139925003052},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04914432764053345}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7656099796295166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7519168853759766},{"id":"https://openalex.org/C12595997","wikidata":"https://www.wikidata.org/wiki/Q739245","display_name":"Extremal graph theory","level":5,"score":0.629152238368988},{"id":"https://openalex.org/C2985318062","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theorem","level":3,"score":0.6262469291687012},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5653315782546997},{"id":"https://openalex.org/C119050217","wikidata":"https://www.wikidata.org/wiki/Q17101806","display_name":"Intersection theorem","level":5,"score":0.5489228367805481},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5404636859893799},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.5036277174949646},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.44847699999809265},{"id":"https://openalex.org/C51044901","wikidata":"https://www.wikidata.org/wiki/Q16680059","display_name":"Strong perfect graph theorem","level":5,"score":0.4438631236553192},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4427146315574646},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.4358361065387726},{"id":"https://openalex.org/C32972407","wikidata":"https://www.wikidata.org/wiki/Q1187620","display_name":"Perfect graph","level":5,"score":0.4252889156341553},{"id":"https://openalex.org/C173644813","wikidata":"https://www.wikidata.org/wiki/Q3527155","display_name":"Robertson\u2013Seymour theorem","level":5,"score":0.42218613624572754},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4039068818092346},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.360828161239624},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.33414924144744873},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.31488752365112305},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.29785633087158203},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.26804929971694946},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.2567480802536011},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.1803314983844757},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.06928139925003052},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04914432764053345},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548325100138","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548325100138","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1444168583","https://openalex.org/W1494308504","https://openalex.org/W1543148594","https://openalex.org/W1986233232","https://openalex.org/W2038398059","https://openalex.org/W2067487847","https://openalex.org/W2069513471","https://openalex.org/W2087476504","https://openalex.org/W2096125244","https://openalex.org/W2096875564","https://openalex.org/W2111007781","https://openalex.org/W2119305988","https://openalex.org/W2121422768","https://openalex.org/W2528023409","https://openalex.org/W3045314401","https://openalex.org/W4280637615"],"related_works":["https://openalex.org/W2147621675","https://openalex.org/W2955976619","https://openalex.org/W610827","https://openalex.org/W4221156011","https://openalex.org/W2039732465","https://openalex.org/W2951841263","https://openalex.org/W1491785597","https://openalex.org/W2051655695","https://openalex.org/W4294006410","https://openalex.org/W2090340868"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Erd\u0151s\u2013Simonovits":[2,20,30],"stability":[3,22,31,34],"theorem":[4,23,35,84],"is":[5,52],"one":[6],"of":[7,44,46,85,107,118],"the":[8,29,42,55,73,104],"most":[9],"widely":[10],"used":[11],"theorems":[12],"in":[13,24,36,94,109],"extremal":[14,56,74],"graph":[15,50],"theory.":[16],"We":[17],"obtain":[18],"an":[19,47],"type":[21],"multi-partite":[25,37,110],"graphs.":[26],"Different":[27],"from":[28,72],"theorem,":[32],"our":[33],"graphs":[38,57,75,111],"says":[39],"that":[40],"if":[41],"number":[43,106],"edges":[45,108],"$H$":[48,59,77],"-free":[49],"$G$":[51,62],"close":[53],"to":[54],"for":[58,76],",":[60],"then":[61],"has":[63],"a":[64,83,92,95,119],"well-defined":[65],"structure":[66],"but":[67],"may":[68],"be":[69],"far":[70],"away":[71],".":[78],"As":[79],"applications,":[80],"we":[81],"strengthen":[82],"Bollob\u00e1s,":[86],"Erd\u0151s,":[87],"and":[88,90,101],"Straus":[89],"solve":[91],"conjecture":[93],"stronger":[96],"form":[97],"posed":[98],"by":[99],"Han":[100],"Zhao":[102],"concerning":[103],"maximum":[105],"which":[112],"does":[113],"not":[114],"contain":[115],"vertex-disjoint":[116],"copies":[117],"clique.":[120]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
