{"id":"https://openalex.org/W2586854929","doi":"https://doi.org/10.37236/6736","title":"Do Triangle-Free Planar Graphs have Exponentially Many $3$-Colorings?","display_name":"Do Triangle-Free Planar Graphs have Exponentially Many $3$-Colorings?","publication_year":2017,"publication_date":"2017-09-08","ids":{"openalex":"https://openalex.org/W2586854929","doi":"https://doi.org/10.37236/6736","mag":"2586854929"},"language":"en","primary_location":{"id":"doi:10.37236/6736","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6736","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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6736","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073630443","display_name":"Zden\u0115k Dvo\u0159\u00e1k","orcid":"https://orcid.org/0000-0002-8308-9746"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Zden\u011bk Dvo\u0159\u00e1k","raw_affiliation_strings":["Computer Science Institute, Charles University, Prague, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Computer Science Institute, Charles University, Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014744746","display_name":"Jean\u2010S\u00e9bastien Sereni","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-S\u00e9bastien Sereni","raw_affiliation_strings":["Centre National de la Recherche Scientifique, LORIA, France"],"affiliations":[{"raw_affiliation_string":"Centre National de la Recherche Scientifique, LORIA, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073630443"],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":null,"apc_paid":null,"fwci":0.7109,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71284733,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"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":0.9372000098228455,"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":0.9372000098228455,"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":0.9286999702453613,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7994730472564697},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7957736253738403},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7318541407585144},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.6884927749633789},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6196043491363525},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5029272437095642},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4793970584869385},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4772194027900696},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4724467396736145},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4541265070438385},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.4207279086112976},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09382960200309753},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07372969388961792},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06686177849769592}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7994730472564697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7957736253738403},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7318541407585144},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.6884927749633789},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6196043491363525},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5029272437095642},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4793970584869385},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4772194027900696},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4724467396736145},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4541265070438385},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.4207279086112976},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09382960200309753},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07372969388961792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06686177849769592},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/6736","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6736","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:1702.00588","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.00588","pdf_url":"https://arxiv.org/pdf/1702.00588","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":"pmh:oai:HAL:hal-01433349v2","is_oa":false,"landing_page_url":"https://hal.science/hal-01433349","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p47/pdf","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.37236/6736","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6736","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":[{"id":"https://openalex.org/G5566021001","display_name":null,"funder_award_id":"P202/12/G061","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W167088980","https://openalex.org/W2475705533","https://openalex.org/W186129870","https://openalex.org/W3200522959","https://openalex.org/W4389944781","https://openalex.org/W2997993211","https://openalex.org/W120415280","https://openalex.org/W4383099232","https://openalex.org/W4301418551","https://openalex.org/W96940172"],"abstract_inverted_index":{"Thomassen":[0],"conjectured":[1],"that":[2,30,63],"triangle-free":[3],"planar":[4,35],"graphs":[5],"have":[6],"an":[7],"exponential":[8],"number":[9],"of":[10,42,55,57],"$3$-colorings.":[11],"We":[12],"show":[13],"this":[14],"conjecture":[15],"to":[16,19,72,82],"be":[17,83],"equivalent":[18],"the":[20,80],"following":[21],"statement:":[22],"there":[23,50],"exists":[24,51],"a":[25,34,40,52],"positive":[26],"real":[27],"$\\alpha$":[28],"such":[29,62],"whenever":[31],"$G$":[32,48],"is":[33,39,66],"graph":[36],"and":[37],"$A$":[38,56],"subset":[41,53],"its":[43],"edges":[44],"whose":[45],"deletion":[46],"makes":[47],"triangle-free,":[49],"$A'$":[54],"size":[58],"at":[59],"least":[60],"$\\alpha|A|$":[61],"$G-(A\\setminus":[64],"A')$":[65],"$3$-colorable.":[67],"This":[68],"equivalence":[69],"allows":[70],"us":[71],"study":[73],"restricted":[74],"situations,":[75],"where":[76],"we":[77],"can":[78],"prove":[79],"statement":[81],"true.":[84]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}