{"id":"https://openalex.org/W2030158164","doi":"https://doi.org/10.1016/0012-365x(73)90142-8","title":"A seven-color theorem on the sphere","display_name":"A seven-color theorem on the sphere","publication_year":1973,"publication_date":"1973-07-01","ids":{"openalex":"https://openalex.org/W2030158164","doi":"https://doi.org/10.1016/0012-365x(73)90142-8","mag":"2030158164"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(73)90142-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(73)90142-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010216203","display_name":"Hudson V. Kronk","orcid":null},"institutions":[{"id":"https://openalex.org/I123946342","display_name":"Binghamton University","ror":"https://ror.org/008rmbt77","country_code":"US","type":"education","lineage":["https://openalex.org/I123946342"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hudson V. Kronk","raw_affiliation_strings":["SUNY at Binghamton, Binghamton, N.Y. 13901, USA","SUNY at Binghamton, Binghamton, N.Y. 13901, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"SUNY at Binghamton, Binghamton, N.Y. 13901, USA","institution_ids":["https://openalex.org/I123946342"]},{"raw_affiliation_string":"SUNY at Binghamton, Binghamton, N.Y. 13901, USA#TAB#","institution_ids":["https://openalex.org/I123946342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081074515","display_name":"John Mitchem","orcid":null},"institutions":[{"id":"https://openalex.org/I51504820","display_name":"San Jose State University","ror":"https://ror.org/04qyvz380","country_code":"US","type":"education","lineage":["https://openalex.org/I51504820"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Mitchem","raw_affiliation_strings":["San Jose State College, San Jose, Calif. 95114, USA","San Jose State College, San Jose, Calif. 95114, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"San Jose State College, San Jose, Calif. 95114, USA","institution_ids":["https://openalex.org/I51504820"]},{"raw_affiliation_string":"San Jose State College, San Jose, Calif. 95114, USA#TAB#","institution_ids":["https://openalex.org/I51504820"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010216203"],"corresponding_institution_ids":["https://openalex.org/I123946342"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.18231427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"5","issue":"3","first_page":"253","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9455999732017517,"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":0.9455999732017517,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.8854531049728394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.844449520111084},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7130811214447021},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6038750410079956},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3449423611164093},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09705260396003723}],"concepts":[{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.8854531049728394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.844449520111084},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7130811214447021},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6038750410079956},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3449423611164093},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09705260396003723},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(73)90142-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(73)90142-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2020422308","https://openalex.org/W2069311964","https://openalex.org/W2083421046","https://openalex.org/W2146117644","https://openalex.org/W2315027061","https://openalex.org/W2799004609","https://openalex.org/W6629172744"],"related_works":["https://openalex.org/W2140509105","https://openalex.org/W3146178872","https://openalex.org/W4235907447","https://openalex.org/W2072835713","https://openalex.org/W4205128724","https://openalex.org/W2040849466","https://openalex.org/W346008744","https://openalex.org/W4284887816","https://openalex.org/W891964471","https://openalex.org/W2484916042"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
