{"id":"https://openalex.org/W7162310121","doi":"https://doi.org/10.1016/j.disopt.2026.100956","title":"The red\u2013blue\u2013yellow matching problem","display_name":"The red\u2013blue\u2013yellow matching problem","publication_year":2026,"publication_date":"2026-05-25","ids":{"openalex":"https://openalex.org/W7162310121","doi":"https://doi.org/10.1016/j.disopt.2026.100956"},"language":"en","primary_location":{"id":"doi:10.1016/j.disopt.2026.100956","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.disopt.2026.100956","pdf_url":null,"source":{"id":"https://openalex.org/S203549655","display_name":"Discrete Optimization","issn_l":"1572-5286","issn":["1572-5286","1873-636X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.disopt.2026.100956","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136946012","display_name":"Manuel Aprile","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manuel Aprile","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086066603","display_name":"Marco Di Summa","orcid":"https://orcid.org/0000-0001-7223-0380"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco Di Summa","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7223-0380","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2760,"currency":"USD","value_usd":2760},"apc_paid":{"value":2760,"currency":"USD","value_usd":2760},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.53451115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":null,"first_page":"100956","last_page":"100956"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.10559999942779541,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12288","display_name":"Optimization and Search Problems","score":0.10559999942779541,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.07940000295639038,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0494999997317791,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6527000069618225},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.625},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5052000284194946},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4431000053882599},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.4275999963283539},{"id":"https://openalex.org/keywords/blossom-algorithm","display_name":"Blossom algorithm","score":0.42640000581741333},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.40290001034736633},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.40220001339912415}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7569000124931335},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6527000069618225},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5198000073432922},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4431000053882599},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42899999022483826},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.4275999963283539},{"id":"https://openalex.org/C61455927","wikidata":"https://www.wikidata.org/wiki/Q1030529","display_name":"Blossom algorithm","level":3,"score":0.42640000581741333},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C100107663","wikidata":"https://www.wikidata.org/wiki/Q1516988","display_name":"Hopcroft\u2013Karp algorithm","level":5,"score":0.396699994802475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3707999885082245},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C72545166","wikidata":"https://www.wikidata.org/wiki/Q10866593","display_name":"3-dimensional matching","level":4,"score":0.3109000027179718},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.26579999923706055}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.disopt.2026.100956","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.disopt.2026.100956","pdf_url":null,"source":{"id":"https://openalex.org/S203549655","display_name":"Discrete Optimization","issn_l":"1572-5286","issn":["1572-5286","1873-636X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2603.18754","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2603.18754","pdf_url":"https://arxiv.org/pdf/2603.18754","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"}],"best_oa_location":{"id":"doi:10.1016/j.disopt.2026.100956","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.disopt.2026.100956","pdf_url":null,"source":{"id":"https://openalex.org/S203549655","display_name":"Discrete Optimization","issn_l":"1572-5286","issn":["1572-5286","1873-636X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4831591238","display_name":null,"funder_award_id":"CUP I53D23002310006","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G6506472545","display_name":null,"funder_award_id":"2022BMBW2A","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320321966","display_name":"Universit\u00e0 degli Studi di Padova","ror":"https://ror.org/00240q980"},{"id":"https://openalex.org/F5497039910","display_name":"Ministero dell'Istruzione e del Merito","ror":"https://ror.org/01ehyh486"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1988698339","https://openalex.org/W1998112574","https://openalex.org/W2079828065","https://openalex.org/W2083246371","https://openalex.org/W2090215490","https://openalex.org/W2123805664","https://openalex.org/W2150547317","https://openalex.org/W2158130018","https://openalex.org/W2174697474","https://openalex.org/W2327315803","https://openalex.org/W2609475100","https://openalex.org/W2610479830","https://openalex.org/W4233756358","https://openalex.org/W4386289171","https://openalex.org/W4387845100"],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,24,59,92,113,130,141,196],"red-blue-yellow":[3,114],"matching":[4,30,63,94,115,128],"problem:":[5],"given":[6],"two":[7],"natural":[8,56,124],"numbers":[9],"$k_R$,":[10],"$k_B$":[11,41],"and":[12,39,44,135,154,167,192],"a":[13,29,55,71,76,109,118,127,147,170,175,184,188],"graph":[14],"$G$":[15,32],"whose":[16,65],"edges":[17,38],"are":[18],"colored":[19],"red,":[20],"blue":[21,42],"or":[22],"yellow,":[23],"goal":[25],"is":[26,45,54,68,146,183],"to":[27,50,91,97],"find":[28],"of":[31,46,58,140,149,162,179,187,199],"that":[33],"contains":[34],"exactly":[35,40,134],"$k_R$":[36],"red":[37],"edges,":[43],"maximum":[47],"cardinality":[48,137],"subject":[49],"these":[51],"constraints.":[52],"This":[53],"generalization":[57],"well":[60],"known":[61,88],"red-blue":[62,93],"problem,":[64,95,116],"complexity":[66],"status":[67],"unknown:":[69],"although":[70],"randomized":[72],"polynomial-time":[73,119],"algorithm":[74,78,121,145],"exists,":[75],"deterministic":[77,89,120],"has":[79,136],"remained":[80],"elusive":[81],"for":[82,112],"nearly":[83],"four":[84],"decades.":[85],"The":[86],"best":[87],"approach":[90],"due":[96],"Yuster":[98],"(2012),":[99],"gives":[100],"an":[101],"additive":[102],"approximation.":[103],"In":[104],"this":[105],"paper,":[106],"we":[107,173],"show":[108],"similar":[110],"result":[111,189],"giving":[117],"that,":[122],"under":[123],"assumptions,":[125],"finds":[126],"satisfying":[129],"color":[131],"requirements":[132],"almost":[133],"within":[138],"3":[139],"optimal":[142],"solution.":[143],"Our":[144],"mix":[148],"classic":[150],"linear":[151],"programming":[152],"techniques":[153],"ad":[155],"hoc":[156],"existence":[157],"results":[158],"on":[159],"restricted":[160],"classes":[161],"graphs":[163],"such":[164],"as":[165],"paths":[166],"cycles.":[168],"As":[169],"key":[171],"ingredient,":[172],"prove":[174],"curious":[176],"topological":[177],"property":[178],"plane":[180],"curves,":[181],"which":[182],"strengthened":[185],"version":[186],"by":[190],"Grandoni":[191],"Zenklusen":[193],"(2010)":[194],"in":[195],"related":[197],"context":[198],"budgeted":[200],"matchings.":[201]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-05-26T00:00:00"}
