{"id":"https://openalex.org/W2166602562","doi":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w","title":"Finding a large hidden clique in a random graph","display_name":"Finding a large hidden clique in a random graph","publication_year":1998,"publication_date":"1998-10-01","ids":{"openalex":"https://openalex.org/W2166602562","doi":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w","mag":"2166602562"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w","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 and 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/A5083469386","display_name":"Noga Alon","orcid":"https://orcid.org/0000-0003-1332-4883"},"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":true,"raw_author_name":"Noga Alon","raw_affiliation_strings":["Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","Research supported in part by a USA Israeli BSF grant, by a grant from the Israel Science Foundation, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Research supported in part by a USA Israeli BSF grant, by a grant from the Israel Science Foundation, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University","institution_ids":[]}]},{"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":true,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","Research supported in part by a Charles Clore Fellowship"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Research supported in part by a Charles Clore Fellowship","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066741544","display_name":"Benny Sudakov","orcid":"https://orcid.org/0000-0003-3307-9475"},"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":true,"raw_author_name":"Benny Sudakov","raw_affiliation_strings":["Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008556299","https://openalex.org/A5066741544","https://openalex.org/A5083469386"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":3.5598,"has_fulltext":false,"cited_by_count":272,"citation_normalized_percentile":{"value":0.93405829,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"13","issue":"3-4","first_page":"457","last_page":"466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9955000281333923,"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":0.9955000281333923,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9950000047683716,"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":0.991599977016449,"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":0.765404224395752},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6101492643356323},{"id":"https://openalex.org/keywords/clique-graph","display_name":"Clique graph","score":0.5681446194648743},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.56600421667099},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5597739815711975},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5281788110733032},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5036076903343201},{"id":"https://openalex.org/keywords/struct","display_name":"struct","score":0.4872950315475464},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4643924832344055},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4486897587776184},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.43302640318870544},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.32200318574905396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2226468026638031},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1677514910697937},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.08850902318954468}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.765404224395752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6101492643356323},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.5681446194648743},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.56600421667099},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5597739815711975},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5281788110733032},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5036076903343201},{"id":"https://openalex.org/C2776142590","wikidata":"https://www.wikidata.org/wiki/Q1164699","display_name":"struct","level":2,"score":0.4872950315475464},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4643924832344055},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4486897587776184},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.43302640318870544},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.32200318574905396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2226468026638031},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1677514910697937},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.08850902318954468},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<457::aid-rsa14>3.0.co;2-w","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 and Algorithms","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2794565019","https://openalex.org/W2264356384","https://openalex.org/W2952246343","https://openalex.org/W1992504234","https://openalex.org/W3080928114","https://openalex.org/W4247942259","https://openalex.org/W2006605460","https://openalex.org/W2049529696","https://openalex.org/W2550802162","https://openalex.org/W2891037262"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,101,111,115],"following":[3],"probabilistic":[4],"model":[5],"of":[6,27,29,43,45,69,114],"a":[7,15,24,37,55],"graph":[8,17],"on":[9,110],"n":[10],"labeled":[11],"vertices.":[12],"First":[13],"choose":[14,22],"random":[16],"G(n,":[18],"1/2),":[19],"and":[20,32,81],"then":[21],"randomly":[23],"subset":[25],"Q":[26,46],"vertices":[28,44],"size":[30],"k":[31],"force":[33],"it":[34],"to":[35,53],"be":[36],"clique":[38,63],"by":[39,47,79,82],"joining":[40],"every":[41],"pair":[42],"an":[48,89],"edge.":[49],"The":[50,106],"problem":[51],"is":[52,108],"give":[54],"polynomial":[56],"time":[57],"algorithm":[58,91,107],"for":[59,66,92,95],"finding":[60],"this":[61,85],"hidden":[62],"almost":[64],"surely":[65],"various":[67,77],"values":[68],"k.":[70],"This":[71],"question":[72],"was":[73],"posed":[74],"independently,":[75],"in":[76],"variants,":[78],"Jerrum":[80],"Ku\u010dera.":[83],"In":[84],"paper":[86],"we":[87],"present":[88],"efficient":[90],"all":[93],"k>cn0.5,":[94],"any":[96],"fixed":[97],"c>0,":[98],"thus":[99],"improving":[100],"trivial":[102],"case":[103],"k>cn0.5(log":[104],"n)0.5.":[105],"based":[109],"spectral":[112],"properties":[113],"graph.":[116],"\u00a9":[117],"1998":[118,129],"John":[119],"Wiley":[120],"&":[121],"Sons,":[122],"Inc.":[123],"Random":[124],"Struct.":[125],"Alg.,":[126],"13:":[127],"457\u2013466,":[128]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":22},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
