{"id":"https://openalex.org/W1709720265","doi":"https://doi.org/10.37236/2435","title":"On $(K_{q},k)$ Stable Graphs with Small $k$","display_name":"On $(K_{q},k)$ Stable Graphs with Small $k$","publication_year":2012,"publication_date":"2012-06-28","ids":{"openalex":"https://openalex.org/W1709720265","doi":"https://doi.org/10.37236/2435","mag":"1709720265"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.37236/2435","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i2p50/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i2p50/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110003079","display_name":"Jean\u2010Luc Fouquet","orcid":null},"institutions":[{"id":"https://openalex.org/I4387153997","display_name":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","ror":"https://ror.org/01nr3td38","country_code":null,"type":"facility","lineage":["https://openalex.org/I12449238","https://openalex.org/I4210143826","https://openalex.org/I4387153997"]},{"id":"https://openalex.org/I4210115196","display_name":"Laboratoire d\u2019Informatique Fondamentale de Marseille","ror":"https://ror.org/022my8t07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210115196","https://openalex.org/I4210142724","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Luc Fouquet","raw_affiliation_strings":["Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","institution_ids":["https://openalex.org/I4387153997","https://openalex.org/I4210115196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053543058","display_name":"Henri Thuillier","orcid":null},"institutions":[{"id":"https://openalex.org/I4387153997","display_name":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","ror":"https://ror.org/01nr3td38","country_code":null,"type":"facility","lineage":["https://openalex.org/I12449238","https://openalex.org/I4210143826","https://openalex.org/I4387153997"]},{"id":"https://openalex.org/I4210115196","display_name":"Laboratoire d\u2019Informatique Fondamentale de Marseille","ror":"https://ror.org/022my8t07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210115196","https://openalex.org/I4210142724","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Henri Thuillier","raw_affiliation_strings":["Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","institution_ids":["https://openalex.org/I4387153997","https://openalex.org/I4210115196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084003710","display_name":"Jean-Marie Vanherpe","orcid":null},"institutions":[{"id":"https://openalex.org/I4387153997","display_name":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","ror":"https://ror.org/01nr3td38","country_code":null,"type":"facility","lineage":["https://openalex.org/I12449238","https://openalex.org/I4210143826","https://openalex.org/I4387153997"]},{"id":"https://openalex.org/I4210115196","display_name":"Laboratoire d\u2019Informatique Fondamentale de Marseille","ror":"https://ror.org/022my8t07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210115196","https://openalex.org/I4210142724","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Marie Vanherpe","raw_affiliation_strings":["Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","institution_ids":["https://openalex.org/I4387153997","https://openalex.org/I4210115196"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080088496","display_name":"A. Pawe\u0142 Wojda","orcid":null},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Adam Pawe\u0142 Wojda","raw_affiliation_strings":["AGH Univ. of Science and Technology, Krakow, Poland"],"affiliations":[{"raw_affiliation_string":"AGH Univ. of Science and Technology, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0,"provenance":"doaj"},"apc_paid":null,"fwci":1.441,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":10,"citation_normalized_percentile":{"value":0.707497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":85,"max":86},"biblio":{"volume":"19","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9848,"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":0.9848,"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":0.9112,"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":0.9058,"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":[],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8235207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6418989},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5710211},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43181932}],"mesh":[],"locations_count":3,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.37236/2435","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i2p50/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://hal.science/hal-00560277","pdf_url":"https://hal.science/hal-00560277/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00934318","pdf_url":"https://hal.science/hal-00934318/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.37236/2435","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i2p50/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":6,"referenced_works":["https://openalex.org/W104732203","https://openalex.org/W2091580321","https://openalex.org/W2178910810","https://openalex.org/W2580817547","https://openalex.org/W2611093227","https://openalex.org/W4251666160"],"related_works":["https://openalex.org/W4245490552","https://openalex.org/W4238204885","https://openalex.org/W3002753104","https://openalex.org/W2142036596","https://openalex.org/W2077600819","https://openalex.org/W2061531152","https://openalex.org/W2042127053","https://openalex.org/W2007980826","https://openalex.org/W1979597421","https://openalex.org/W1587224694"],"abstract_inverted_index":{"A":[0],"graph":[1,49,78],"$G$":[2],"is":[3,53,82],"$(K_{q},k)$":[4],"stable":[5,29,48,77],"if":[6],"it":[7],"contains":[8],"a":[9,21],"copy":[10],"of":[11,17],"$K_{q}$":[12],"after":[13],"deleting":[14],"any":[15],"subset":[16],"$k$":[18],"vertices.":[19],"In":[20],"previous":[22],"paper":[23],"we":[24,41],"have":[25,42],"characterized":[26],"the":[27,45,74],"$(K_q,k)$":[28,47,76],"graphs":[30],"with":[31,50,79],"minimum":[32,51,80],"size":[33,52,81],"for":[34,55,66],"$3":[35],"\\le":[36,38,61,72],"q":[37],"5$":[39,58],"and":[40,59,70],"proved":[43],"that":[44,65],"only":[46,75],"$K_{q+k}$":[54],"$q":[56,67],"\\ge":[57,68],"$k":[60,71],"3$.":[62],"We":[63],"show":[64],"6$":[69],"\\frac{q}{2}+1$":[73],"isomorphic":[83],"to":[84],"$K_{q+k}$.":[85]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1709720265","counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2024-12-24T17:52:35.941974","created_date":"2016-06-24"}