{"id":"https://openalex.org/W7169602711","doi":"https://doi.org/10.48550/arxiv.2607.14694","title":"Acyclic Dichromatic Number of Tournaments: these are the Champions","display_name":"Acyclic Dichromatic Number of Tournaments: these are the Champions","publication_year":2026,"publication_date":"2026-07-16","ids":{"openalex":"https://openalex.org/W7169602711","doi":"https://doi.org/10.48550/arxiv.2607.14694"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.14694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.14694","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2607.14694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141069470","display_name":"Pierre Aboulker","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aboulker, Pierre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015923364","display_name":"Pierre Charbit","orcid":"https://orcid.org/0000-0001-9401-040X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charbit, Pierre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093685341","display_name":"Samuel Coulomb","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Coulomb, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039192445","display_name":"Kathryn Nurse","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nurse, Kathryn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5141074390","display_name":"Lucas Picasarri-Arrieta","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Picasarri-Arrieta, Lucas","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":0.6805999875068665,"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":0.6805999875068665,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.08799999952316284,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.05429999902844429,"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/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.8766000270843506},{"id":"https://openalex.org/keywords/tournament","display_name":"Tournament","score":0.769599974155426},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7117000222206116},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6126999855041504},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4099999964237213}],"concepts":[{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.8766000270843506},{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.769599974155426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7177000045776367},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7117000222206116},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6855999827384949},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6126999855041504},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45989999175071716},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4099999964237213},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.2572999894618988}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.14694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.14694","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.14694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.14694","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"acyclic":[1,36,51,66],"dichromatic":[2,52,67],"number":[3,68],"of":[4,12,58],"an":[5],"oriented":[6,28],"graph":[7],"is":[8],"the":[9,17,27,40],"minimum":[10],"size":[11],"a":[13,56,70],"vertex-partition":[14],"such":[15],"that":[16,42,65],"digraphs":[18],"induced":[19],"by":[20],"any":[21,32],"single":[22],"part":[23],"are":[24,35],"acyclic,":[25],"and":[26,61,63],"bipartite":[29],"graphs":[30],"between":[31],"two":[33],"parts":[34],"too.":[37],"We":[38],"characterize":[39],"subtournaments":[41],"must":[43],"appear":[44],"in":[45],"every":[46],"tournament":[47],"with":[48],"sufficiently":[49],"large":[50],"number,":[53],"thereby":[54],"confirming":[55],"conjecture":[57],"Bang-Jensen,":[59],"Picasarri-Arrieta,":[60],"Yeo":[62],"prove":[64],"satisfies":[69],"local":[71],"to":[72],"global":[73],"property.":[74]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-18T00:00:00"}
