{"id":"https://openalex.org/W2170487340","doi":"https://doi.org/10.1007/s00224-009-9231-5","title":"Why Almost All k-Colorable Graphs Are Easy to Color","display_name":"Why Almost All k-Colorable Graphs Are Easy to Color","publication_year":2009,"publication_date":"2009-08-03","ids":{"openalex":"https://openalex.org/W2170487340","doi":"https://doi.org/10.1007/s00224-009-9231-5","mag":"2170487340"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-009-9231-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-009-9231-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","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/A5044991483","display_name":"Amin Coja\u2010Oghlan","orcid":"https://orcid.org/0000-0002-7350-1418"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Amin Coja-Oghlan","raw_affiliation_strings":["School of Informatics, University of Edinburgh, Edinburgh, UK"],"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Edinburgh, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008556299","display_name":"Michael Krivelevich","orcid":"https://orcid.org/0000-0003-2357-4982"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel","School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067064621","display_name":"Dan Vilenchik","orcid":"https://orcid.org/0000-0002-3895-688X"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dan Vilenchik","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA","Department of Mathematics, UCLA, Los Angeles, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067064621"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.414,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.8273279,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"46","issue":"3","first_page":"523","last_page":"565"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983999729156494,"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":0.9983999729156494,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9887999892234802,"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":0.9833999872207642,"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/combinatorics","display_name":"Combinatorics","score":0.69877028465271},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.6923245191574097},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6106906533241272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.555016040802002},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5504216551780701},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.5378465056419373},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5238475799560547},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.47039684653282166},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4570378065109253},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.4542255699634552},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43351465463638306},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.43026143312454224},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4166554808616638},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3862374722957611},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26363420486450195},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1301547884941101},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.10703161358833313},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.05020001530647278}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.69877028465271},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.6923245191574097},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6106906533241272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.555016040802002},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5504216551780701},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.5378465056419373},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5238475799560547},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.47039684653282166},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4570378065109253},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.4542255699634552},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43351465463638306},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.43026143312454224},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4166554808616638},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3862374722957611},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26363420486450195},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1301547884941101},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.10703161358833313},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.05020001530647278},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00224-009-9231-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-009-9231-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:43211","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.2225","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.2225","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~vilenchi/papers/2007/UniformKCol_journal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.9542","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.9542","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~krivelev/colkk.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.81.6840","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.81.6840","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~krivelev/colkk.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W99448414","https://openalex.org/W1504923017","https://openalex.org/W1526818805","https://openalex.org/W1537769454","https://openalex.org/W1547089046","https://openalex.org/W1831211001","https://openalex.org/W1854875838","https://openalex.org/W1971493102","https://openalex.org/W1980276492","https://openalex.org/W1982531027","https://openalex.org/W1987178221","https://openalex.org/W1988522098","https://openalex.org/W2012724629","https://openalex.org/W2016776056","https://openalex.org/W2021145763","https://openalex.org/W2026709222","https://openalex.org/W2058422149","https://openalex.org/W2063428816","https://openalex.org/W2079035346","https://openalex.org/W2082249316","https://openalex.org/W2083883919","https://openalex.org/W2088272899","https://openalex.org/W2088419249","https://openalex.org/W2103012681","https://openalex.org/W2115885909","https://openalex.org/W2130763052","https://openalex.org/W2139919528","https://openalex.org/W2295468341","https://openalex.org/W2740374147","https://openalex.org/W2950654313","https://openalex.org/W3029388252","https://openalex.org/W3140660692","https://openalex.org/W4233413206","https://openalex.org/W4243880374","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W4229747356","https://openalex.org/W398688634","https://openalex.org/W1542397451","https://openalex.org/W3169197204","https://openalex.org/W2380525562","https://openalex.org/W4297911588","https://openalex.org/W4320918672","https://openalex.org/W133702489","https://openalex.org/W2527418013"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
