{"id":"https://openalex.org/W7155525541","doi":"https://doi.org/10.48550/arxiv.2604.21025","title":"A Complexity Dichotomy for Generalized Rainbow Matchings Based on Color Classes","display_name":"A Complexity Dichotomy for Generalized Rainbow Matchings Based on Color Classes","publication_year":2026,"publication_date":"2026-04-22","ids":{"openalex":"https://openalex.org/W7155525541","doi":"https://doi.org/10.48550/arxiv.2604.21025"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.21025","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21025","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.21025","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068100133","display_name":"Felix Hommelsheim","orcid":"https://orcid.org/0000-0003-4444-9793"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hommelsheim, Felix","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134494962","display_name":"Pia Jehmlich","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jehmlich, Pia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075980018","display_name":"Moritz M\u00fchlenthaler","orcid":"https://orcid.org/0000-0002-2729-127X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M\u00fchlenthaler, Moritz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.5583999752998352,"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":0.5583999752998352,"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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.13130000233650208,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.05999999865889549,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multipartite","display_name":"Multipartite","score":0.6816999912261963},{"id":"https://openalex.org/keywords/rainbow","display_name":"Rainbow","score":0.4950000047683716},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.45980000495910645},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.459199994802475},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.44690001010894775},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42820000648498535},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.4235000014305115},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.42149999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7610999941825867},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7458000183105469},{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.6816999912261963},{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.4950000047683716},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48489999771118164},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.459199994802475},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.44690001010894775},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42820000648498535},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.4235000014305115},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.42149999737739563},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.37229999899864197},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C7036158","wikidata":"https://www.wikidata.org/wiki/Q3385162","display_name":"Graph homomorphism","level":5,"score":0.31119999289512634},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.30570000410079956},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.28519999980926514},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.2768000066280365},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.26179999113082886}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.21025","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21025","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.21025","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21025","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Given":[0],"an":[1,134],"edge-colored":[2],"graph,":[3],"the":[4,15,28,37,40,67,70,76,152,156,161,185],"Maximum":[5,43],"Rainbow":[6,44],"Matching":[7,45],"problem":[8,34,77,162],"asks":[9],"for":[10,32,137,141],"a":[11,47,56,86,94,99,105,167,196,201],"maximum-cardinality":[12],"matching":[13,95,203],"of":[14,39,69,96,147,155],"graph":[16,59,128],"that":[17,75,91,116,160,175,199],"contains":[18],"at":[19,205],"most":[20,206],"one":[21],"edge":[22],"from":[23,209],"each":[24,210],"color.":[25],"We":[26,107],"provide":[27,195],"following":[29],"complexity":[30,139],"dichotomy":[31],"this":[33,110,123],"based":[35],"on":[36,88,101],"structure":[38],"color":[41,53,83,114,178,189,211],"classes:":[42],"admits":[46],"polynomial-time":[48,197],"algorithm":[49,198],"if":[50,81],"almost":[51,176],"every":[52,82],"class":[54,84,212],"is":[55,62,85,92],"complete":[57,119,181,192],"multipartite":[58,120,182],"and":[60,144],"it":[61],"NP-hard":[63,79],"otherwise.":[64],"To":[65,150],"prove":[66,151],"NP-hardness-part":[68],"dichotomy,":[71,157],"we":[72,125,158,172,194],"first":[73],"show":[74,159],"remains":[78],"even":[80],"subgraph":[87],"four":[89,102],"vertices":[90,103],"either":[93],"size":[97],"two,":[98],"path":[100],"or":[104],"paw.":[106],"then":[108],"leverage":[109],"result":[111],"to":[112,132,165],"all":[113,177,188],"classes":[115,179,190],"are":[117,180,191],"not":[118],"graphs.":[121,183],"For":[122],"purpose,":[124],"introduce":[126],"color-closed":[127],"classes,":[129],"which":[130],"seem":[131],"be":[133,146],"appropriate":[135],"notion":[136],"obtaining":[138],"classifications":[140],"rainbow":[142],"problems":[143],"may":[145],"independent":[148],"interest.":[149],"positive":[153],"part":[154],"essentially":[163],"reduces":[164],"computing":[166],"maximum":[168,202],"$(l,":[169],"u)$-matching,":[170],"where":[171,187],"heavily":[173],"exploit":[174],"In":[184],"case":[186],"multipartite,":[193],"computes":[200],"containing":[204],"$m_i$":[207],"edges":[208],"$i$.":[213]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-25T00:00:00"}
