{"id":"https://openalex.org/W1509174822","doi":"https://doi.org/10.1007/s00493-019-3268-0","title":"Girth Six Cubic Graphs Have Petersen Minors","display_name":"Girth Six Cubic Graphs Have Petersen Minors","publication_year":2019,"publication_date":"2019-10-28","ids":{"openalex":"https://openalex.org/W1509174822","doi":"https://doi.org/10.1007/s00493-019-3268-0","mag":"1509174822"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-019-3268-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-019-3268-0","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1405.0533","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019299318","display_name":"Neil Robertson","orcid":"https://orcid.org/0000-0002-9230-6124"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Neil Robertson","raw_affiliation_strings":["Department of Mathematics, Ohio State University, 231 W. 18th Ave., Columbus, Ohio, 43210, USA","Department of Mathematics, Ohio State University, Columbus, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ohio State University, 231 W. 18th Ave., Columbus, Ohio, 43210, USA","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Department of Mathematics, Ohio State University, Columbus, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031948088","display_name":"Paul Seymour","orcid":"https://orcid.org/0000-0003-0067-4534"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. D. Seymour","raw_affiliation_strings":["Department of Mathematics, Princeton University, Princeton, New Jersey, 08544, USA","Department of Mathematics, Princeton University, Princeton, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Princeton, New Jersey, 08544, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Mathematics, Princeton University, Princeton, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101892672","display_name":"Robin Thomas","orcid":"https://orcid.org/0000-0002-9318-1458"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robin Thomas","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332, USA","School of Mathematics  Georgia Institute of Technology, Atlanta, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of Mathematics  Georgia Institute of Technology, Atlanta, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"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":2,"citation_normalized_percentile":{"value":0.00012388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"39","issue":"6","first_page":"1413","last_page":"1423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9984999895095825,"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/T10849","display_name":"Finite Group Theory Research","score":0.9973999857902527,"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/cubic-graph","display_name":"Cubic graph","score":0.5300614237785339},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.4939940571784973},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4937504231929779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41222119331359863},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.05778518319129944}],"concepts":[{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.5300614237785339},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.4939940571784973},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4937504231929779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41222119331359863},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.05778518319129944},{"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/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00493-019-3268-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-019-3268-0","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1405.0533","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1405.0533","pdf_url":"https://arxiv.org/pdf/1405.0533","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:1509174822","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1405.0533.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:CiteSeerX.psu:10.1.1.49.4535","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.4535","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.gatech.edu/~thomas/girth.ps","raw_type":"text"},{"id":"doi:10.48550/arxiv.1405.0533","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1405.0533","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1405.0533","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1405.0533","pdf_url":"https://arxiv.org/pdf/1405.0533","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1589210857","https://openalex.org/W1991592444","https://openalex.org/W2067669580","https://openalex.org/W2962748025"],"related_works":["https://openalex.org/W2982032523","https://openalex.org/W2054731897","https://openalex.org/W2055492581","https://openalex.org/W2166193462","https://openalex.org/W2103478523","https://openalex.org/W1583399499","https://openalex.org/W3036508010","https://openalex.org/W2232156287","https://openalex.org/W2060903069","https://openalex.org/W2041100538","https://openalex.org/W2057023080","https://openalex.org/W3143106334","https://openalex.org/W1990419188","https://openalex.org/W2382285921","https://openalex.org/W3043244511","https://openalex.org/W2394181405","https://openalex.org/W2017043109","https://openalex.org/W2359867666","https://openalex.org/W2774641548","https://openalex.org/W2005225976"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
