{"id":"https://openalex.org/W3010722852","doi":"https://doi.org/10.37236/9448","title":"Cooperative Conditions for the Existence of Rainbow Matchings","display_name":"Cooperative Conditions for the Existence of Rainbow Matchings","publication_year":2022,"publication_date":"2022-01-28","ids":{"openalex":"https://openalex.org/W3010722852","doi":"https://doi.org/10.37236/9448","mag":"3010722852"},"language":"en","primary_location":{"id":"doi:10.37236/9448","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9448","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p23/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/v29i1p23/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059026447","display_name":"Ron Aharoni","orcid":"https://orcid.org/0000-0002-1768-1901"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Ron Aharoni","raw_affiliation_strings":["Technion - Israel Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Technion - Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054387266","display_name":"Joseph Briggs","orcid":"https://orcid.org/0000-0002-6919-5817"},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph Briggs","raw_affiliation_strings":["Auburn University"],"affiliations":[{"raw_affiliation_string":"Auburn University","institution_ids":["https://openalex.org/I82497590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102834292","display_name":"Minho Cho","orcid":"https://orcid.org/0000-0002-7751-2165"},"institutions":[{"id":"https://openalex.org/I4210099236","display_name":"Kootenay Association for Science & Technology","ror":"https://ror.org/011pv9p44","country_code":"CA","type":"nonprofit","lineage":["https://openalex.org/I4210099236"]},{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["CA","KR"],"is_corresponding":false,"raw_author_name":"Minho Cho","raw_affiliation_strings":["KAIST"],"affiliations":[{"raw_affiliation_string":"KAIST","institution_ids":["https://openalex.org/I4210099236","https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080229875","display_name":"Jinha Kim","orcid":"https://orcid.org/0000-0001-5982-7836"},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jinha Kim","raw_affiliation_strings":["Institute for Basic Science"],"affiliations":[{"raw_affiliation_string":"Institute for Basic Science","institution_ids":["https://openalex.org/I4210104335"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059026447"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.4526,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62767273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"29","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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":0.9925000071525574,"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/rainbow","display_name":"Rainbow","score":0.9005153179168701},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8771120309829712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8644051551818848},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8322603702545166},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6196385025978088},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5405271649360657},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5346369743347168},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3711061477661133},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04997369647026062}],"concepts":[{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.9005153179168701},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8771120309829712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8644051551818848},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8322603702545166},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6196385025978088},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5405271649360657},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5346369743347168},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3711061477661133},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04997369647026062},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":1,"locations":[{"id":"doi:10.37236/9448","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9448","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p23/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:10.37236/9448","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9448","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p23/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/G1993186149","display_name":"Combinatorial Structures and Processes","funder_award_id":"823748","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2689612763","display_name":null,"funder_award_id":"Marie","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3034753964","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G3290884034","display_name":null,"funder_award_id":"409/16","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G342704958","display_name":null,"funder_award_id":"funded","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G3942910960","display_name":null,"funder_award_id":"(NRF) grant","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G4405413065","display_name":null,"funder_award_id":"2023464","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G4956428346","display_name":null,"funder_award_id":"Horizon 2020 research and innovatio","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5036817778","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innov","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5404998627","display_name":null,"funder_award_id":"Chair","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5758617376","display_name":null,"funder_award_id":"IBS-R029-C1","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G6064893360","display_name":null,"funder_award_id":"202346","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G626505518","display_name":null,"funder_award_id":"No. 201","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G6840542549","display_name":null,"funder_award_id":"1162/15","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G6929685529","display_name":null,"funder_award_id":"IBS-R029-C","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G6977260880","display_name":"EFFECT OF NATURAL VIRAL RNA SEQUENCE VARIATION ON INFLUENZA VIRUS RNA FUNCTION","funder_award_id":"201607","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7315415636","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7685055460","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G7718105100","display_name":null,"funder_award_id":"BS-R029-C1","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G7746946551","display_name":null,"funder_award_id":"1357/16","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7789814769","display_name":null,"funder_award_id":"162/15","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G781745418","display_name":null,"funder_award_id":"326/16","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8633428685","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innovat","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G982292920","display_name":null,"funder_award_id":"NRF-20","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320326441","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3010722852.pdf","grobid_xml":"https://content.openalex.org/works/W3010722852.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1506619093","https://openalex.org/W1984879308","https://openalex.org/W2009820428","https://openalex.org/W2024498264","https://openalex.org/W2040229317","https://openalex.org/W2090096177","https://openalex.org/W2132220587","https://openalex.org/W2199773171","https://openalex.org/W2963734391","https://openalex.org/W2963868941","https://openalex.org/W3102903967","https://openalex.org/W4287823954","https://openalex.org/W6602147907"],"related_works":["https://openalex.org/W4300815962","https://openalex.org/W2949690312","https://openalex.org/W128077073","https://openalex.org/W2567825307","https://openalex.org/W4295762832","https://openalex.org/W1592682627","https://openalex.org/W2785998768","https://openalex.org/W2945016732","https://openalex.org/W2371352078","https://openalex.org/W2362975861"],"abstract_inverted_index":{"Let":[0],"$k>1$,":[1],"and":[2,53,63],"let":[3],"$\\mathcal{F}$":[4,26],"be":[5,56],"a":[6,15,28,65],"family":[7],"of":[8,12,21,25,30,39],"$2n+k-3$":[9,43],"non-empty":[10],"sets":[11],"edges":[13],"in":[14,74],"bipartite":[16],"graph.":[17],"If":[18],"the":[19,46,76,81],"union":[20],"every":[22],"$k$":[23],"members":[24],"contains":[27],"matching":[29,38],"size":[31,40],"$n$,":[32],"then":[33],"there":[34],"exists":[35],"an":[36],"$\\mathcal{F}$-rainbow":[37],"$n$.":[41],"Replacing":[42],"by":[44,64],"$2n+k-2$,":[45],"result":[47,82],"is":[48,73],"true":[49],"also":[50],"for":[51],"$k=1$,":[52],"it":[54],"can":[55],"proved":[57],"(for":[58],"all":[59],"$k$)":[60],"both":[61],"topologically":[62],"relatively":[66],"simple":[67],"combinatorial":[68],"argument.":[69],"The":[70],"main":[71],"effort":[72],"gaining":[75],"last":[77],"$1$,":[78],"which":[79],"makes":[80],"sharp.":[83]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}