{"id":"https://openalex.org/W2018948753","doi":"https://doi.org/10.1137/120877817","title":"${4,5}$ Is Not Coverable: A Counterexample to a Conjecture of Kaiser and \u0160krekovski","display_name":"${4,5}$ Is Not Coverable: A Counterexample to a Conjecture of Kaiser and \u0160krekovski","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2018948753","doi":"https://doi.org/10.1137/120877817","mag":"2018948753"},"language":"en","primary_location":{"id":"doi:10.1137/120877817","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120877817","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5076267412","display_name":"Roman \u010cada","orcid":"https://orcid.org/0000-0002-6283-2975"},"institutions":[{"id":"https://openalex.org/I92715842","display_name":"University of West Bohemia in Pilsen","ror":"https://ror.org/040t43x18","country_code":"CZ","type":"education","lineage":["https://openalex.org/I92715842"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Roman \u010cada","raw_affiliation_strings":["#N#University of West Bohemia#N#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N#University of West Bohemia#N#","institution_ids":["https://openalex.org/I92715842"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112906621","display_name":"Shuya Chiba","orcid":null},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shuya Chiba","raw_affiliation_strings":["Tokyo University of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokyo University of Science","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080040800","display_name":"Kenta Ozeki","orcid":"https://orcid.org/0000-0003-3118-0086"},"institutions":[{"id":"https://openalex.org/I4210086780","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19","country_code":"JP","type":"government","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210086780"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kenta Ozeki","raw_affiliation_strings":["Japan Science and Technology Agency"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Japan Science and Technology Agency","institution_ids":["https://openalex.org/I4210086780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041544249","display_name":"Petr Vr\u00e1na","orcid":"https://orcid.org/0000-0001-9246-474X"},"institutions":[{"id":"https://openalex.org/I92715842","display_name":"University of West Bohemia in Pilsen","ror":"https://ror.org/040t43x18","country_code":"CZ","type":"education","lineage":["https://openalex.org/I92715842"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Petr Vr\u00e1na","raw_affiliation_strings":["#N#University of West Bohemia#N#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N#University of West Bohemia#N#","institution_ids":["https://openalex.org/I92715842"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080322469","display_name":"Kiyoshi Yoshimoto","orcid":"https://orcid.org/0000-0002-1142-375X"},"institutions":[{"id":"https://openalex.org/I104946051","display_name":"Nihon University","ror":"https://ror.org/05jk51a88","country_code":"JP","type":"education","lineage":["https://openalex.org/I104946051"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kiyoshi Yoshimoto","raw_affiliation_strings":["Nihon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nihon University","institution_ids":["https://openalex.org/I104946051"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08342685,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"27","issue":"1","first_page":"141","last_page":"144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9984999895095825,"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/conjecture","display_name":"Conjecture","score":0.7968015670776367},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.7443292140960693},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6794780492782593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5885522365570068},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5578907132148743},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49049872159957886}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7968015670776367},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7443292140960693},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6794780492782593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5885522365570068},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5578907132148743},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49049872159957886}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120877817","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120877817","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G114474212","display_name":"A STUDY ON THE EXISTENCE OF VERTEX-DISJOINT STARS IN GRAPHS","funder_award_id":"23740087","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G867486213","display_name":"On Thomassen's conjecture and 2-factors of claw-free graphs","funder_award_id":"22540152","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1515064769","https://openalex.org/W1967979192","https://openalex.org/W1994519017","https://openalex.org/W2016461386","https://openalex.org/W2024011816","https://openalex.org/W2037189698","https://openalex.org/W2041826321","https://openalex.org/W2041928734","https://openalex.org/W2057023080","https://openalex.org/W2088720699","https://openalex.org/W2142881856","https://openalex.org/W2176625698","https://openalex.org/W2253259020","https://openalex.org/W4236890056"],"related_works":["https://openalex.org/W4309222106","https://openalex.org/W2012590989","https://openalex.org/W4385681624","https://openalex.org/W4240581084","https://openalex.org/W2049141591","https://openalex.org/W2952569802","https://openalex.org/W2950489642","https://openalex.org/W1734188852","https://openalex.org/W4297939726","https://openalex.org/W4298858221"],"abstract_inverted_index":{"For":[0],"a":[1,10,19,54],"subset":[2],"$A$":[3,42],"of":[4,7],"the":[5,58],"set":[6],"positive":[8],"integers,":[9],"graph":[11],"$G$":[12,17,36],"is":[13,43,78],"called":[14],"$A$-coverable":[15],"if":[16,48],"has":[18],"cycle":[20,60],"(a":[21],"subgraph":[22],"in":[23,35,66],"which":[24,30,103],"all":[25,32,49],"vertices":[26],"have":[27],"even":[28],"degree)":[29],"intersects":[31],"edge-cuts":[33],"$T$":[34],"with":[37],"$|T|":[38],"\\in":[39],"A$,":[40],"and":[41,63,92],"said":[44],"to":[45,57],"be":[46],"coverable":[47],"graphs":[50,102],"are":[51,104],"$A$-coverable.":[52],"As":[53],"possible":[55],"approach":[56],"dominating":[59],"conjecture,":[61],"Kaiser":[62,91],"\u0160krekovski":[64],"conjectured":[65],"[SIAM":[67],"J.":[68],"Discrete":[69],"Math.,":[70],"22":[71],"(2008),":[72],"pp.":[73],"861--874]":[74],"that":[75,97],"$\\mathbb{N}":[76,81],"+3$":[77],"coverable,":[79],"where":[80],"+3":[82],"=":[83],"\\{4,5,6,":[84],"\\ldots\\}$.":[85],"In":[86],"this":[87],"paper,":[88],"we":[89],"disprove":[90],"\u0160krekovski's":[93],"conjecture":[94],"by":[95],"showing":[96],"there":[98],"exist":[99],"infinitely":[100],"many":[101],"not":[105],"$\\{4,5\\}$-coverable.":[106]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
