{"id":"https://openalex.org/W7211890435","doi":"https://doi.org/10.48550/arxiv.2609.04956","title":"The Erd\u0151s-P\u00f3sa Property for Colorful Minors","display_name":"The Erd\u0151s-P\u00f3sa Property for Colorful Minors","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7211890435","doi":"https://doi.org/10.48550/arxiv.2609.04956"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04956","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04956","pdf_url":"https://arxiv.org/pdf/2609.04956","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.04956","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030571814","display_name":"Evangelos Protopapas","orcid":"https://orcid.org/0000-0003-0294-2985","observed_orcids":["https://orcid.org/0000-0003-0294-2985"]},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Protopapas, Evangelos","raw_affiliation_strings":["Faculty of Mathematics, Informatics and Mechanics , University of Warsaw , Poland","\u2016"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Informatics and Mechanics , University of Warsaw , Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"\u2016","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085447779","display_name":"Dimitrios M. Thilikos","orcid":"https://orcid.org/0000-0003-0470-1800","observed_orcids":["https://orcid.org/0000-0003-0470-1800"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4405261681"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Thilikos, Dimitrios M.","raw_affiliation_strings":["LIRMM , Univ Montpellier , CNRS , Montpellier , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIRMM , Univ Montpellier , CNRS , Montpellier , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210101743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065969392","display_name":"Sebastian Wiederrecht","orcid":"https://orcid.org/0000-0003-0462-7815","observed_orcids":["https://orcid.org/0000-0003-0462-7815"]},"institutions":[{"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":["KR"],"is_corresponding":false,"raw_author_name":"Wiederrecht, Sebastian","raw_affiliation_strings":["KAIST , School of Computing , Daejeon , South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KAIST , School of Computing , Daejeon , South Korea","institution_ids":["https://openalex.org/I157485424"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9922000169754028,"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":0.9922000169754028,"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":0.006899999920278788,"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":0.00019999999494757503,"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/erdos-posa-property","display_name":"Erd\u0151s-P\u00f3sa property","score":0.9750000238418579},{"id":"https://openalex.org/keywords/graph-minors","display_name":"graph minors","score":0.8450000286102295},{"id":"https://openalex.org/keywords/graph-contraction","display_name":"graph contraction","score":0.6240000128746033},{"id":"https://openalex.org/keywords/planar-graphs","display_name":"planar graphs","score":0.6100000143051147},{"id":"https://openalex.org/keywords/robertson-seymour-theorem","display_name":"Robertson-Seymour theorem","score":0.8790000081062317},{"id":"https://openalex.org/keywords/obstruction-sets","display_name":"obstruction sets","score":0.5270000100135803},{"id":"https://openalex.org/keywords/network-visualization","display_name":"network visualization","score":0.4350000023841858}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6639999747276306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6516000032424927},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5997999906539917},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.5327000021934509},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49619999527931213},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4372999966144562},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4171999990940094},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.3059000074863434},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.26980000734329224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04956","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04956","pdf_url":"https://arxiv.org/pdf/2609.04956","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,"listed_in":[],"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":"doi:10.48550/arxiv.2609.04956","doi":"https://doi.org/10.48550/arxiv.2609.04956","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04956","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.04956","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04956","pdf_url":"https://arxiv.org/pdf/2609.04956","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1136415967","display_name":"PIQ","funder_award_id":"ANR-24-RRII-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1190173965","display_name":null,"funder_award_id":"France2030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1302621641","display_name":"Unifying Theories for Multivariate Algorithms","funder_award_id":"ANR-20-CE92-0027","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1938303756","display_name":null,"funder_award_id":"IBS\u2010R029\u2010C1","funder_id":"https://openalex.org/F4320326441","funder_display_name":"Institute for Basic Science"},{"id":"https://openalex.org/G3994523055","display_name":"Ordered graphs, decompositions, algorithms and structures","funder_award_id":"ANR-24-CE48-4377","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5296751580","display_name":null,"funder_award_id":"ANR-20","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320326441","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211890435.pdf","grobid_xml":"https://content.openalex.org/works/W7211890435.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W2020381865","https://openalex.org/W2057826895","https://openalex.org/W2071321409","https://openalex.org/W2075199819","https://openalex.org/W2104713819","https://openalex.org/W2332112754","https://openalex.org/W2738178211","https://openalex.org/W2931394993","https://openalex.org/W2962772870","https://openalex.org/W2963079069","https://openalex.org/W3159948484","https://openalex.org/W4400222930","https://openalex.org/W4404849849","https://openalex.org/W4414742193","https://openalex.org/W7134839685","https://openalex.org/W7223728368"],"related_works":["https://openalex.org/W2116038678","https://openalex.org/W4414742193","https://openalex.org/W2885601953","https://openalex.org/W7172523889","https://openalex.org/W7095990285","https://openalex.org/W2931394993","https://openalex.org/W4404849849","https://openalex.org/W3088551598","https://openalex.org/W4400024540","https://openalex.org/W117909350"],"abstract_inverted_index":{"A":[0,37],"colorful":[1,67,72,89,171,182],"graph":[2,38],"relation":[3,7],"enhances":[4],"the":[5,17,40,66,75,88,92,170,181,185,189],"minor":[6,68],"by":[8,15,52,127],"merging":[9],"color":[10],"sets":[11],"along":[12,118],"contractions":[13],"and":[14,25,46,58,108],"allowing":[16],"removal":[18],"of":[19,56,137,143,154,161,173,175,178,184],"colors;":[20],"it":[21,49],"generalizes":[22],"rooted":[23],"minors":[24,44,172],"models":[26],"problems":[27],"on":[28,105],"graphs":[29,73,90],"with":[30,91,100],"several,":[31],"possibly":[32],"overlapping,":[33],"annotated":[34],"vertex":[35],"sets.":[36],"has":[39],"Erd\u0151s-P\u00f3sa":[41,76],"property":[42,93],"for":[43,65,156],"if":[45,48],"only":[47,145],"is":[50,86,125,165],"planar,":[51],"a":[53,113,152],"classical":[54,190],"theorem":[55],"Robertson":[57],"Seymour.":[59],"In":[60],"this":[61],"work":[62],"we":[63],"determine,":[64],"relation,":[69],"exactly":[70,169],"which":[71,144],"have":[74,148],"property.":[77],"Our":[78],"characterization":[79],"takes":[80],"three":[81],"equivalent":[82],"forms.":[83],"The":[84,123,163],"first":[85],"structural:":[87],"are":[94,132,151,168],"those":[95,133],"that":[96,119,150,187],"can":[97],"be":[98],"drawn":[99],"all":[101],"their":[102],"colored":[103],"vertices":[104],"one":[106],"face":[107,120],"whose":[109],"colors":[110,149],"are,":[111],"in":[112],"precise":[114],"sense,":[115],"laid":[116],"out":[117],"without":[121],"interleaving.":[122],"second":[124],"given":[126],"an":[128,138],"obstruction":[129],"set:":[130],"they":[131,167],"excluding":[134],"every":[135,157],"member":[136],"explicit":[139],"infinite":[140],"family":[141],"$\\mathcal{O},$":[142],"$\\mathbf{O}(|I|^{4})$":[146],"members":[147],"subset":[153],"$I,$":[155],"finite":[158],"set":[159],"$I$":[160],"colors.":[162],"third":[164],"grid-like:":[166],"unions":[174],"particular":[176],"families":[177],"segregated":[179],"grids,":[180],"analogues":[183],"grids":[186],"drive":[188],"proof.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}
