{"id":"https://openalex.org/W2571300421","doi":"https://doi.org/10.37236/6923","title":"Majority Choosability of Digraphs","display_name":"Majority Choosability of Digraphs","publication_year":2017,"publication_date":"2017-09-22","ids":{"openalex":"https://openalex.org/W2571300421","doi":"https://doi.org/10.37236/6923","mag":"2571300421"},"language":"en","primary_location":{"id":"doi:10.37236/6923","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6923","pdf_url":null,"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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6923","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090591126","display_name":"Marcin Anholcer","orcid":"https://orcid.org/0000-0001-7322-7095"},"institutions":[{"id":"https://openalex.org/I12379730","display_name":"Pozna\u0144 University of Economics and Business","ror":"https://ror.org/0532c1x92","country_code":"PL","type":"education","lineage":["https://openalex.org/I12379730"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marcin Anholcer","raw_affiliation_strings":["Poznan University of Economics and Business","Pozna\u0144\u201e University of Economics and Business"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Poznan University of Economics and Business","institution_ids":["https://openalex.org/I12379730"]},{"raw_affiliation_string":"Pozna\u0144\u201e University of Economics and Business","institution_ids":["https://openalex.org/I12379730"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038469350","display_name":"Bart\u0142omiej Bosek","orcid":"https://orcid.org/0000-0001-8756-3663"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Bart\u0142omiej Bosek","raw_affiliation_strings":["Jagiellonian University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jagiellonian University","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033531626","display_name":"Jaros\u0142aw Grytczuk","orcid":"https://orcid.org/0000-0002-0258-6143"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jaros\u0142aw Grytczuk","raw_affiliation_strings":["Warsaw University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Warsaw University of Technology","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02407096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"3","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":0.967199981212616,"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":0.967199981212616,"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/digraph","display_name":"Digraph","score":0.9597058296203613},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8229261636734009},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7109570503234863},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.694917619228363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6709138751029968},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.6470218896865845},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.6057915091514587},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.5807287096977234},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.5492029190063477},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4176599681377411},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.1539340615272522}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.9597058296203613},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8229261636734009},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7109570503234863},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.694917619228363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6709138751029968},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.6470218896865845},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.6057915091514587},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.5807287096977234},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.5492029190063477},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4176599681377411},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.1539340615272522},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/6923","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6923","pdf_url":null,"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"},{"id":"pmh:oai:arXiv.org:1608.06912","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1608.06912","pdf_url":"https://arxiv.org/pdf/1608.06912","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2571300421","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1608.06912.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:ruj.uj.edu.pl:item/47013","is_oa":true,"landing_page_url":"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p57/pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1608.06912","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1608.06912","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":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/6923","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6923","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2025484786","https://openalex.org/W2057094213","https://openalex.org/W2506307253"],"related_works":["https://openalex.org/W2963686871","https://openalex.org/W3009339632","https://openalex.org/W3102625287","https://openalex.org/W1566398300","https://openalex.org/W2002209708","https://openalex.org/W50813256","https://openalex.org/W1930391967","https://openalex.org/W2229287010","https://openalex.org/W2558716804","https://openalex.org/W3012864922","https://openalex.org/W2052903450","https://openalex.org/W2212115383","https://openalex.org/W2884495715","https://openalex.org/W2437364787","https://openalex.org/W2120784503","https://openalex.org/W2806544754","https://openalex.org/W2743756977","https://openalex.org/W3202909567","https://openalex.org/W3195649555","https://openalex.org/W14232539"],"abstract_inverted_index":{"A":[0,32],"majority":[1,36,55,68,104,160],"coloring":[2,8,56,120],"of":[3,9,21,24,42,44,46,57,97,124,132,135],"a":[4,7,54,72,76,95,98,119],"digraph":[5,33,66,117,158],"is":[6,35,53,67,106,159],"its":[10,139],"vertices":[11,51],"such":[12],"that":[13,64,115,156],"for":[14,39],"each":[15],"vertex":[16,137],"$v$,":[17],"at":[18,129],"most":[19,130],"half":[20],"the":[22,27,50,111,133,147],"out-neighbors":[23,134],"$v$":[25],"have":[26],"same":[28,148],"color":[29],"as":[30,94],"$v$.":[31],"$D$":[34,58],"$k$-choosable":[37],"if":[38],"any":[40,136],"assignment":[41],"lists":[43,123],"colors":[45],"size":[47,125],"$k$":[48],"to":[49,75],"there":[52],"from":[59,121],"these":[60],"lists.":[61],"We":[62,90],"prove":[63],"every":[65,116,157],"$4$-choosable.":[69],"This":[70,141],"gives":[71],"positive":[73],"answer":[74],"question":[77],"posed":[78,145],"recently":[79],"by":[80,146],"Kreutzer,":[81],"Oum,":[82],"Seymour,":[83],"van":[84],"der":[85],"Zypen,":[86],"and":[87,150],"Wood":[88],"(2017).":[89],"obtain":[91],"this":[92],"result":[93],"consequence":[96],"more":[99],"general":[100],"theorem,":[101],"in":[102,127],"which":[103,128],"condition":[105],"profitably":[107],"extended.":[108],"For":[109],"instance,":[110],"theorem":[112],"implies":[113],"also":[114],"has":[118],"arbitrary":[122],"three,":[126],"$2/3$":[131],"share":[138],"color.":[140],"solves":[142],"another":[143],"problem":[144],"authors,":[149],"supports":[151],"an":[152],"intriguing":[153],"conjecture":[154],"stating":[155],"$3$-colorable.":[161]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}