{"id":"https://openalex.org/W2088210486","doi":"https://doi.org/10.1007/bf02122682","title":"The chromatic number of random graphs at the double-jump threshold","display_name":"The chromatic number of random graphs at the double-jump threshold","publication_year":1989,"publication_date":"1989-03-01","ids":{"openalex":"https://openalex.org/W2088210486","doi":"https://doi.org/10.1007/bf02122682","mag":"2088210486"},"language":"en","primary_location":{"id":"doi:10.1007/bf02122682","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02122682","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":["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/A5003433063","display_name":"Tomasz \u0141uczak","orcid":"https://orcid.org/0000-0002-3517-9034"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"T. \u0141uczak","raw_affiliation_strings":["Institute of Mathematics, Adam Mickiewicz University, Poznan, Poland","Institute of Mathematics ADAM Mickiewicz University Pozna\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Adam Mickiewicz University, Poznan, Poland","institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I59411706"]},{"raw_affiliation_string":"Institute of Mathematics ADAM Mickiewicz University Pozna\u0144, Poland","institution_ids":["https://openalex.org/I59411706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064543263","display_name":"John C. Wierman","orcid":"https://orcid.org/0000-0002-5000-9455"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. C. Wierman","raw_affiliation_strings":["Department of Mathematical Sciences, John Hopkins University, Baltimore, Maryland, USA","Department of Mathematical Sciences, John Hopkins University, Baltimore, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, John Hopkins University, Baltimore, Maryland, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Department of Mathematical Sciences, John Hopkins University, Baltimore, USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2513,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.87161125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"1","first_page":"39","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9911999702453613,"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/mathematics","display_name":"Mathematics","score":0.893031120300293},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.743004322052002},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6227203607559204},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5814810991287231},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5060493350028992},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4734853506088257},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.44469451904296875},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.4379051923751831},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.43111446499824524},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4230923056602478},{"id":"https://openalex.org/keywords/planarity-testing","display_name":"Planarity testing","score":0.41194969415664673},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4104929566383362},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3511778712272644},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.30008456110954285},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09035730361938477}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.893031120300293},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.743004322052002},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6227203607559204},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5814810991287231},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5060493350028992},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4734853506088257},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.44469451904296875},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.4379051923751831},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.43111446499824524},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4230923056602478},{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.41194969415664673},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4104929566383362},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3511778712272644},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30008456110954285},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09035730361938477},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02122682","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02122682","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W631645519","https://openalex.org/W1600475114","https://openalex.org/W2001735302","https://openalex.org/W2017552248","https://openalex.org/W2069802496","https://openalex.org/W2070658523","https://openalex.org/W2616697817","https://openalex.org/W2905110430","https://openalex.org/W3107687480"],"related_works":["https://openalex.org/W603403972","https://openalex.org/W2061237693","https://openalex.org/W1554245510","https://openalex.org/W4285762950","https://openalex.org/W2239518402","https://openalex.org/W2083238533","https://openalex.org/W2152638828","https://openalex.org/W3121955789","https://openalex.org/W2564891670","https://openalex.org/W1578113210"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}