{"id":"https://openalex.org/W2754813585","doi":"https://doi.org/10.37236/5185","title":"Stability for Vertex Cycle Covers","display_name":"Stability for Vertex Cycle Covers","publication_year":2017,"publication_date":"2017-09-08","ids":{"openalex":"https://openalex.org/W2754813585","doi":"https://doi.org/10.37236/5185","mag":"2754813585"},"language":"en","primary_location":{"id":"doi:10.37236/5185","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5185","pdf_url":null,"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://doi.org/10.37236/5185","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108264183","display_name":"J\u00f3zsef Balogh","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J\u00f3zsef Balogh","raw_affiliation_strings":["University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055318466","display_name":"Frank Mousset","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Frank Mousset","raw_affiliation_strings":["ETH Zurich"],"affiliations":[{"raw_affiliation_string":"ETH Zurich","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017513172","display_name":"Jozef Skokan","orcid":"https://orcid.org/0000-0003-3996-7676"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jozef Skokan","raw_affiliation_strings":["LSE and University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"LSE and University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108264183"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.0195,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.73178919,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","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":0.9983000159263611,"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":0.9983000159263611,"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":0.9732999801635742,"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":0.9001893997192383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7950188517570496},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5784923434257507},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4871384799480438},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4602592885494232},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39646244049072266},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08686777949333191}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9001893997192383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7950188517570496},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5784923434257507},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4871384799480438},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4602592885494232},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39646244049072266},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08686777949333191},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/5185","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5185","pdf_url":null,"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"},{"id":"pmh:oai:eprints.lse.ac.uk:84218","is_oa":false,"landing_page_url":"https://orcid.org/0000-0003-3996-7676>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":{"id":"doi:10.37236/5185","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5185","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W4301429470","https://openalex.org/W2168900540","https://openalex.org/W2125310826","https://openalex.org/W2380536887","https://openalex.org/W2399035783"],"abstract_inverted_index":{"In":[0],"1996":[1],"Kouider":[2],"and":[3,58,97,165,212],"Lonc":[4],"proved":[5],"the":[6,41,46,115,127,144,154,213],"following":[7,155],"natural":[8],"generalization":[9],"of":[10,88,191,200],"Dirac's":[11],"Theorem:":[12],"for":[13,196],"any":[14],"integer":[15],"$k\\geq":[16],"2$,":[17],"if":[18,158],"$G$":[19,36,161],"is":[20,43,71,122],"an":[21,85,123],"$n$-vertex":[22,51,124],"graph":[23,80,92,125,160],"with":[24,65,84,101,126],"minimum":[25,55,94,166],"degree":[26,56,95,167],"at":[27],"least":[28],"$n/k$,":[29,169],"then":[30,170],"there":[31,49,135],"are":[32,50,136],"$k-1$":[33,63,174],"cycles":[34,64,175],"in":[35,45],"that":[37,48,53,59,134,140,203],"together":[38],"cover":[39],"all":[40,177],"vertices.This":[42],"tight":[44],"sense":[47],"graphs":[52],"have":[54],"$n/k-1$":[57,96],"do":[60],"not":[61],"contain":[62],"this":[66,130,148],"property.":[67],"A":[68],"concrete":[69],"example":[70],"given":[72,108,146],"by":[73,147],"$I_{n,k}":[74],"=":[75],"K_n\\setminus":[76],"K_{(k-1)n/k+1}$":[77],"(an":[78],"edge-maximal":[79],"on":[81],"$n$":[82,163],"vertices":[83,164],"independent":[86],"set":[87],"size":[89],"$(k-1)n/k+1$).":[90],"This":[91],"has":[93,162],"cannot":[98],"be":[99,183],"covered":[100],"fewer":[102],"than":[103],"$k$":[104],"cycles.":[105],"More":[106,150],"generally,":[107],"positive":[109,201],"integers":[110,202],"$k_1,\\dotsc,k_r$":[111,199],"summing":[112],"to":[113,188,205],"$k$,":[114],"disjoint":[116],"union":[117],"$I_{k_1n/k,k_1}+":[118,192],"\\dotsb":[119,193],"+":[120,194],"I_{k_rn/k,k_r}$":[121],"same":[128],"properties.In":[129],"paper,":[131],"we":[132,152],"show":[133],"no":[137],"extremal":[138],"examples":[139],"differ":[141],"substantially":[142],"from":[143],"ones":[145],"construction.":[149],"precisely,":[151],"obtain":[153],"stability":[156],"result:":[157],"a":[159,189],"nearly":[168],"it":[171,181],"either":[172],"contains":[173],"covering":[176],"vertices,":[178],"or":[179],"else":[180],"must":[182],"close":[184],"(in":[185],"\u2018edit":[186],"distance')":[187],"subgraph":[190],"I_{k_rn/k,k_r}$,":[195],"some":[197],"sequence":[198],"sum":[204],"$k$.Our":[206],"proof":[207],"uses":[208],"Szemer\u00e9di's":[209],"Regularity":[210],"Lemma":[211],"related":[214],"machinery.":[215]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
