{"id":"https://openalex.org/W3138472971","doi":"https://doi.org/10.37236/10529","title":"On Factors of Independent Transversals in $k$-Partite Graphs","display_name":"On Factors of Independent Transversals in $k$-Partite Graphs","publication_year":2021,"publication_date":"2021-11-18","ids":{"openalex":"https://openalex.org/W3138472971","doi":"https://doi.org/10.37236/10529","mag":"3138472971"},"language":"en","primary_location":{"id":"doi:10.37236/10529","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10529","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p23/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":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p23/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Raphael Yuster","raw_affiliation_strings":["Department of Mathematics University of Haifa Haifa 3498838, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Haifa Haifa 3498838, Israel","institution_ids":["https://openalex.org/I91203450"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026016357"],"corresponding_institution_ids":["https://openalex.org/I91203450"],"apc_list":null,"apc_paid":null,"fwci":0.6184,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59786477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"28","issue":"4","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":0.9998999834060669,"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":0.9998999834060669,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987000226974487,"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":0.8879293203353882},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7373272180557251},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6870930194854736},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5864217877388},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5182385444641113},{"id":"https://openalex.org/keywords/transversal","display_name":"Transversal (combinatorics)","score":0.4978830814361572},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47057005763053894},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46483537554740906},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.46478271484375},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.46463847160339355},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4340882897377014}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8879293203353882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7373272180557251},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6870930194854736},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5864217877388},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5182385444641113},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.4978830814361572},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47057005763053894},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46483537554740906},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.46478271484375},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.46463847160339355},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4340882897377014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10529","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10529","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p23/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"},{"id":"pmh:oai:arXiv.org:2103.09139","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.09139","pdf_url":"https://arxiv.org/pdf/2103.09139","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3138472971","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2103.09139.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2103.09139","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.09139","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/10529","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10529","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p23/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3138472971.pdf","grobid_xml":"https://content.openalex.org/works/W3138472971.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1957375148","https://openalex.org/W1965408599","https://openalex.org/W1965802316","https://openalex.org/W1990479896","https://openalex.org/W1993446652","https://openalex.org/W2008097118","https://openalex.org/W2029374777","https://openalex.org/W2067394129","https://openalex.org/W2067487847","https://openalex.org/W2090326703","https://openalex.org/W2096875564","https://openalex.org/W2146017177","https://openalex.org/W3010388516","https://openalex.org/W3105644180","https://openalex.org/W3154417085","https://openalex.org/W3207089107"],"related_works":["https://openalex.org/W3042836143","https://openalex.org/W2759171057","https://openalex.org/W2947834848","https://openalex.org/W2084452371","https://openalex.org/W3103288299","https://openalex.org/W2963251415","https://openalex.org/W2271661788","https://openalex.org/W2964073220","https://openalex.org/W2744540962","https://openalex.org/W1993531838","https://openalex.org/W2950834709","https://openalex.org/W2955563424","https://openalex.org/W2952991316","https://openalex.org/W2942436526","https://openalex.org/W3122488962","https://openalex.org/W2544865958","https://openalex.org/W3197800973","https://openalex.org/W3083477460","https://openalex.org/W2214401133","https://openalex.org/W1798393124"],"abstract_inverted_index":{"A":[0,44],"$[k,n,1]$-graph":[1,67],"is":[2,22,32,49,90,96,116,129],"a":[3,23,30,41,50,69,99,156],"$k$-partite":[4],"graph":[5,15,31],"with":[6],"parts":[7,21],"of":[8,20,46,52,71,158],"order":[9],"$n$":[10,53],"such":[11,29,64],"that":[12,36,65,82,109,125,146],"the":[13,60,126,132,140],"bipartite":[14],"induced":[16],"by":[17],"any":[18],"pair":[19],"matching.":[24],"An":[25],"independent":[26,34,47,55,72],"transversal":[27],"in":[28,40,119],"an":[33],"set":[35,51],"intersects":[37],"each":[38],"part":[39],"single":[42],"vertex.":[43],"factor":[45,70],"transversals":[48,73],"pairwise-disjoint":[54],"transversals.":[56],"Let":[57],"$f(k)$":[58],"be":[59],"smallest":[61],"integer":[62],"$n_0$":[63],"every":[66],"has":[68],"assuming":[74],"$n":[75],"\\geqslant":[76,85],"n_0$.":[77],"Several":[78],"known":[79,117],"conjectures":[80],"imply":[81],"for":[83,131,150],"$k":[84],"2$,":[86],"$f(k)=k$":[87],"if":[88,94],"$k$":[89,95,152],"even":[91],"and":[92,118,144],"$f(k)=k+1$":[93],"odd.":[97],"While":[98],"simple":[100],"greedy":[101,133,141],"algorithm":[102,142],"based":[103],"on":[104],"iterating":[105],"Hall's":[106],"Theorem":[107],"shows":[108],"$f(k)":[110,147],"\\leqslant":[111,148],"2k-2$,":[112],"no":[113],"better":[114],"bound":[115,127,143],"fact,":[120],"there":[121],"are":[122],"instances":[123],"showing":[124],"$2k-2$":[128],"tight":[130],"algorithm.":[134],"Here":[135],"we":[136],"significantly":[137],"improve":[138],"upon":[139],"prove":[145],"1.78k$":[149],"all":[151],"sufficiently":[153],"large,":[154],"answering":[155],"question":[157],"MacKeigan.":[159]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
