{"id":"https://openalex.org/W4213277474","doi":"https://doi.org/10.1016/s0022-0000(03)00120-x","title":"Almost all graphs with average degree 4 are 3-colorable","display_name":"Almost all graphs with average degree 4 are 3-colorable","publication_year":2003,"publication_date":"2003-09-01","ids":{"openalex":"https://openalex.org/W4213277474","doi":"https://doi.org/10.1016/s0022-0000(03)00120-x"},"language":"en","primary_location":{"id":"doi:10.1016/s0022-0000(03)00120-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0022-0000(03)00120-x","pdf_url":null,"source":{"id":"https://openalex.org/S141020589","display_name":"Journal of Computer and System Sciences","issn_l":"0022-0000","issn":["0022-0000","1090-2724"],"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":"Journal of Computer and System Sciences","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/A5021300666","display_name":"Dimitris Achlioptas","orcid":"https://orcid.org/0000-0003-2349-822X"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dimitris Achlioptas","raw_affiliation_strings":["Microsoft Research, Redmond, Washington, USA"],"affiliations":[{"raw_affiliation_string":"Microsoft Research, Redmond, Washington, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008033989","display_name":"Cristopher Moore","orcid":"https://orcid.org/0000-0002-2062-1942"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]},{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cristopher Moore","raw_affiliation_strings":["Computer Science Department, University of New Mexico, Farris Engineering Center, Albuquerque, NM 87131, USA","Santa Fe Institute, Santa Fe, NM, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of New Mexico, Farris Engineering Center, Albuquerque, NM 87131, USA","institution_ids":["https://openalex.org/I169521973"]},{"raw_affiliation_string":"Santa Fe Institute, Santa Fe, NM, USA","institution_ids":["https://openalex.org/I1308548392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008033989"],"corresponding_institution_ids":["https://openalex.org/I1308548392","https://openalex.org/I169521973"],"apc_list":{"value":2520,"currency":"USD","value_usd":2520},"apc_paid":null,"fwci":1.4538,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.83560913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"2","first_page":"441","last_page":"471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9936000108718872,"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/combinatorics","display_name":"Combinatorics","score":0.7284318804740906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7110922336578369},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7075057625770569},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.557966411113739},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5354908108711243},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.5044244527816772},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5005984306335449},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.47899648547172546},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4714934229850769},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4687877893447876},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.4292569160461426},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2446369230747223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2048293650150299},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.10267496109008789},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08851945400238037},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.047305166721343994}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7284318804740906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7110922336578369},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7075057625770569},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.557966411113739},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5354908108711243},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.5044244527816772},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5005984306335449},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.47899648547172546},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4714934229850769},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4687877893447876},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.4292569160461426},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2446369230747223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2048293650150299},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.10267496109008789},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08851945400238037},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.047305166721343994},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0022-0000(03)00120-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0022-0000(03)00120-x","pdf_url":null,"source":{"id":"https://openalex.org/S141020589","display_name":"Journal of Computer and System Sciences","issn_l":"0022-0000","issn":["0022-0000","1090-2724"],"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":"Journal of Computer and System Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1515766261","https://openalex.org/W1534808934","https://openalex.org/W1854875838","https://openalex.org/W1979720612","https://openalex.org/W1988522098","https://openalex.org/W1997698259","https://openalex.org/W2010309395","https://openalex.org/W2029712200","https://openalex.org/W2044881936","https://openalex.org/W2048267719","https://openalex.org/W2062259223","https://openalex.org/W2065663455","https://openalex.org/W2077154649","https://openalex.org/W2083116175","https://openalex.org/W2125103654","https://openalex.org/W2128782263","https://openalex.org/W2132647359","https://openalex.org/W2152026596","https://openalex.org/W2167036627","https://openalex.org/W2963332217","https://openalex.org/W3037173771","https://openalex.org/W3143219376"],"related_works":["https://openalex.org/W2157783000","https://openalex.org/W4287117052","https://openalex.org/W4206705200","https://openalex.org/W2963009577","https://openalex.org/W2788975631","https://openalex.org/W2028363955","https://openalex.org/W3176308333","https://openalex.org/W2903402681","https://openalex.org/W2124568589","https://openalex.org/W2061237693"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
