{"id":"https://openalex.org/W1558198855","doi":"https://doi.org/10.37236/3252","title":"Erd\u00f6s-Gy\u00e1rf\u00e1s Conjecture for Cubic Planar Graphs","display_name":"Erd\u00f6s-Gy\u00e1rf\u00e1s Conjecture for Cubic Planar Graphs","publication_year":2013,"publication_date":"2013-04-09","ids":{"openalex":"https://openalex.org/W1558198855","doi":"https://doi.org/10.37236/3252","mag":"1558198855"},"language":"en","primary_location":{"id":"doi:10.37236/3252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p7/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p7/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082251997","display_name":"Christopher Heckman","orcid":"https://orcid.org/0000-0002-5948-2978"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christopher Carl Heckman","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 - 1804","School of Mathematical and Statistical Sciences; Arizona State University; Tempe AZ 85287-1804"],"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 - 1804","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"School of Mathematical and Statistical Sciences; Arizona State University; Tempe AZ 85287-1804","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084540189","display_name":"Roi Krakovski","orcid":null},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Roi Krakovski","raw_affiliation_strings":["Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel","Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082251997"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.03756691,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"20","issue":"2","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":0.9987999796867371,"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":0.9987999796867371,"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":0.9782999753952026,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9545000195503235,"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/conjecture","display_name":"Conjecture","score":0.8377646803855896},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7986781001091003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7591551542282104},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.7588669657707214},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.737611711025238},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6647666692733765},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5489138960838318},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5292548537254333},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5178990364074707},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43052399158477783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11745434999465942},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.10573408007621765}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8377646803855896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7986781001091003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7591551542282104},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.7588669657707214},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.737611711025238},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6647666692733765},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5489138960838318},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5292548537254333},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5178990364074707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43052399158477783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11745434999465942},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.10573408007621765},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"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":1,"locations":[{"id":"doi:10.37236/3252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p7/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/3252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p7/pdf","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":null,"license_id":null,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1558198855.pdf","grobid_xml":"https://content.openalex.org/works/W1558198855.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1827591251","https://openalex.org/W2123293563"],"related_works":["https://openalex.org/W3216105633","https://openalex.org/W1701875187","https://openalex.org/W2990956612","https://openalex.org/W2886427884","https://openalex.org/W4240422189","https://openalex.org/W1983209214","https://openalex.org/W3066943322","https://openalex.org/W2221235787","https://openalex.org/W2964336346","https://openalex.org/W4245930683"],"abstract_inverted_index":{"In":[0,34],"1995,":[1],"Paul":[2],"Erd\u00f6s":[3],"and":[4,55],"Andr\u00e1s":[5],"Gy\u00e1rf\u00e1s":[6],"conjectured":[7],"that":[8,25,39],"for":[9,43],"every":[10],"graph":[11],"of":[12,31],"minimum":[13],"degree":[14],"at":[15],"least":[16],"3,":[17],"there":[18],"exists":[19],"a":[20,28,61],"non-negative":[21],"integer":[22],"$m$":[23],"such":[24],"$G$":[26],"contains":[27],"simple":[29],"cycle":[30],"length":[32],"$2^m$.":[33],"this":[35],"paper,":[36],"we":[37],"prove":[38],"the":[40,57],"conjecture":[41],"holds":[42],"3-connected":[44],"cubic":[45],"planar":[46],"graphs.":[47],"The":[48],"proof":[49],"is":[50],"long,":[51],"computer-based":[52],"in":[53,60],"parts,":[54],"employs":[56],"Discharging":[58],"Method":[59],"novel":[62],"way.":[63]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":21},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
