{"id":"https://openalex.org/W2156924276","doi":"https://doi.org/10.1002/rsa.3240010403","title":"Small cliques in random graphs","display_name":"Small cliques in random graphs","publication_year":1990,"publication_date":"1990-12-01","ids":{"openalex":"https://openalex.org/W2156924276","doi":"https://doi.org/10.1002/rsa.3240010403","mag":"2156924276"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240010403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240010403","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","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/A5103407000","display_name":"A. D. Barbour","orcid":null},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"A. D. Barbour","raw_affiliation_strings":["Institut fu\u0308r Angewandte Mathematik, Universita\u0308t Zu\u0308rich, Ra\u0308mistrasse 74, CH-8001 Zu\u0308rich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institut fu\u0308r Angewandte Mathematik, Universita\u0308t Zu\u0308rich, Ra\u0308mistrasse 74, CH-8001 Zu\u0308rich, Switzerland","institution_ids":["https://openalex.org/I202697423"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022615833","display_name":"Svante Janson","orcid":"https://orcid.org/0000-0002-9680-2790"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Svante Janson","raw_affiliation_strings":["Department of Mathematics, Uppsala University, Thunbergsva\u0308gen 3, S-752 38 Uppsala, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, Thunbergsva\u0308gen 3, S-752 38 Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110883614","display_name":"Micha\u0142 Karo\u0144ski","orcid":null},"institutions":[{"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":"Michal Karo\u0144ski","raw_affiliation_strings":["Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, Poznan\u0301, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, Poznan\u0301, Poland","institution_ids":["https://openalex.org/I59411706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078267731","display_name":"Andrzej Ruci\u0144ski","orcid":"https://orcid.org/0000-0002-0742-7694"},"institutions":[{"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":"Andrzej Ruci\u0144ski","raw_affiliation_strings":["Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, Poznan\u0301, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, Poznan\u0301, Poland","institution_ids":["https://openalex.org/I59411706"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103407000"],"corresponding_institution_ids":["https://openalex.org/I202697423"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.3633,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.64839606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"1","issue":"4","first_page":"403","last_page":"434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9997000098228455,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8252065181732178},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.7581402063369751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7330466508865356},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5523762702941895},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5358304977416992},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5086139440536499},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.4754447937011719},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4667385518550873},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43938884139060974},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.41457709670066833},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.31767529249191284},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1566646695137024},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.13836735486984253},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.06804513931274414}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8252065181732178},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.7581402063369751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7330466508865356},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5523762702941895},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5358304977416992},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5086139440536499},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.4754447937011719},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4667385518550873},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43938884139060974},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.41457709670066833},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.31767529249191284},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1566646695137024},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.13836735486984253},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.06804513931274414}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/rsa.3240010403","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240010403","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:www.zora.uzh.ch:22879","is_oa":false,"landing_page_url":"https://www.zora.uzh.ch/22879","pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Barbour, A D; Janson, S; Karonski, M; Rucinski, A  (1990). Small cliques in random graphs.  Random Structures & Algorithms, 1(4):403-434.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1964940671","https://openalex.org/W1968989096","https://openalex.org/W1983809492","https://openalex.org/W2033787071","https://openalex.org/W2081877251","https://openalex.org/W2082286519","https://openalex.org/W2156549096","https://openalex.org/W2802739963","https://openalex.org/W4237187777","https://openalex.org/W4241669766","https://openalex.org/W4297584681","https://openalex.org/W4299533062"],"related_works":["https://openalex.org/W1493037708","https://openalex.org/W4289672287","https://openalex.org/W2972046864","https://openalex.org/W4385327816","https://openalex.org/W1995233739","https://openalex.org/W2009862268","https://openalex.org/W4288278989","https://openalex.org/W2888394449","https://openalex.org/W2963574048","https://openalex.org/W1504268228"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"d":[2,6,15,36],"\u2265":[3],"1,":[4],"a":[5,9,13],"\u2010clique":[7],"in":[8,20,38],"graph":[10,42],"G":[11,43],"is":[12],"complete":[14,23],"\u2010vertex":[16],"subgraph":[17,24],"not":[18],"contained":[19],"any":[21],"larger":[22],"of":[25,32,35],"G.":[26],"We":[27],"investigate":[28],"the":[29,33,39],"limit":[30],"distribution":[31],"number":[34],"\u2010cliques":[37],"binomial":[40],"random":[41],"(":[44,51],"n,":[45],"p":[46,48,50],"),":[47,53],"=":[49],"n":[52,54],"\u2192\u221e.":[55]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}