{"id":"https://openalex.org/W1543013432","doi":"https://doi.org/10.37236/4717","title":"Strong Tur\u00e1n Stability","display_name":"Strong Tur\u00e1n Stability","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1543013432","doi":"https://doi.org/10.37236/4717","mag":"1543013432"},"language":"en","primary_location":{"id":"doi:10.37236/4717","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4717","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i3p9/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i3p9/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009339365","display_name":"Mykhaylo Tyomkyn","orcid":"https://orcid.org/0000-0002-3491-4068"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Mykhaylo Tyomkyn","raw_affiliation_strings":["University of Birmingham","University of Birmingham.*"],"affiliations":[{"raw_affiliation_string":"University of Birmingham","institution_ids":["https://openalex.org/I79619799"]},{"raw_affiliation_string":"University of Birmingham.*","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002846888","display_name":"Andrew J. Uzzell","orcid":null},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew J. Uzzell","raw_affiliation_strings":["University of Nebraska - Lincoln","#N##TAB##TAB##TAB##TAB# University of Nebraska-Lincoln#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"University of Nebraska - Lincoln","institution_ids":["https://openalex.org/I114395901"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Nebraska-Lincoln#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009339365"],"corresponding_institution_ids":["https://openalex.org/I79619799"],"apc_list":null,"apc_paid":null,"fwci":1.3535,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.74608783,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"22","issue":"3","first_page":null,"last_page":null},"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":0.9994999766349792,"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":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9682999849319458,"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/T11476","display_name":"Graph theory and applications","score":0.9617999792098999,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8939687609672546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8772428035736084},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.7388632297515869},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.69499671459198},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5592740774154663},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5496339797973633},{"id":"https://openalex.org/keywords/stability-theorem","display_name":"Stability theorem","score":0.4205380082130432},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36394816637039185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04686036705970764}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8939687609672546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8772428035736084},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.7388632297515869},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.69499671459198},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5592740774154663},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5496339797973633},{"id":"https://openalex.org/C2985318062","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theorem","level":3,"score":0.4205380082130432},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36394816637039185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04686036705970764},{"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:10.37236/4717","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4717","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i3p9/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/4717","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4717","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i3p9/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8683756101","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322327","funder_display_name":"Knut och Alice Wallenbergs Stiftelse"},{"id":"https://openalex.org/G8718021159","display_name":null,"funder_award_id":"EP/K033379/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8724254536","display_name":"Robustness of properties of random and pseudo-random graphs","funder_award_id":"EP/K033379/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320324119","display_name":"Uppsala Universitet","ror":"https://ror.org/048a87296"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1543013432.pdf","grobid_xml":"https://content.openalex.org/works/W1543013432.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W345637930","https://openalex.org/W1607720736","https://openalex.org/W1676972809","https://openalex.org/W1986746825","https://openalex.org/W2027470314","https://openalex.org/W2059872504","https://openalex.org/W2062230178","https://openalex.org/W2074920973","https://openalex.org/W2157534638","https://openalex.org/W2164548535","https://openalex.org/W2168685161","https://openalex.org/W2327268113","https://openalex.org/W2476848496","https://openalex.org/W2978070068","https://openalex.org/W4234124733","https://openalex.org/W6600020421","https://openalex.org/W6609665257","https://openalex.org/W6611572904","https://openalex.org/W6638847059"],"related_works":["https://openalex.org/W2376029318","https://openalex.org/W2388301251","https://openalex.org/W2013770701","https://openalex.org/W3013941779","https://openalex.org/W1998659141","https://openalex.org/W3195376785","https://openalex.org/W2066375965","https://openalex.org/W3178681420","https://openalex.org/W4298227579","https://openalex.org/W2111927753"],"abstract_inverted_index":{"We":[0,11],"study":[1],"maximal":[2],"$K_{r+1}$-free":[3,69],"graphs":[4,70],"$G$":[5,17,33],"of":[6,23,32,59,62,67,71],"almost":[7],"extremal":[8,68],"size\u2014typically,":[9],"$e(G)=\\operatorname{ex}(n,K_{r+1})-O(n)$.":[10],"show":[12],"that":[13],"any":[14],"such":[15],"graph":[16],"must":[18,34],"have":[19,35,46],"a":[20,51,55,60],"large":[21],"amount":[22],"`symmetry':":[24],"in":[25],"particular,":[26],"all":[27,78],"but":[28],"very":[29],"few":[30],"vertices":[31,38],"twins.":[36],"(Two":[37],"$u$":[39],"and":[40],"$v$":[41],"are":[42],"twins":[43],"if":[44],"they":[45],"the":[47,65],"same":[48],"neighbourhood.)":[49],"As":[50],"corollary,":[52],"we":[53],"obtain":[54],"new,":[56],"short":[57],"proof":[58],"theorem":[61],"Simonovits":[63],"on":[64],"structure":[66],"chromatic":[72],"number":[73],"at":[74],"least":[75],"$k$":[76],"for":[77],"fixed":[79],"$k":[80],"\\geq":[81,83],"r":[82],"2$.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
