{"id":"https://openalex.org/W1988142136","doi":"https://doi.org/10.1002/1098-2418(200008)17:1<1::aid-rsa1>3.0.co;2-4","title":"Sharp thresholds for certain Ramsey properties of random graphs","display_name":"Sharp thresholds for certain Ramsey properties of random graphs","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1988142136","doi":"https://doi.org/10.1002/1098-2418(200008)17:1<1::aid-rsa1>3.0.co;2-4","mag":"1988142136"},"language":"en","primary_location":{"id":"doi:10.1002/1098-2418(200008)17:1<1::aid-rsa1>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1098-2418(200008)17:1<1::aid-rsa1>3.0.co;2-4","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/A5111578201","display_name":"Ehud Friedgut","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ehud Friedgut","raw_affiliation_strings":["Department of Computer Science, University of California, Berkeley, CA 94720","Research done partially at the Institute for Advanced Study, Princeton, and supported by the State of New Jersey and the von Hoffmann, Arcana foundation"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Research done partially at the Institute for Advanced Study, Princeton, and supported by the State of New Jersey and the von Hoffmann, Arcana foundation","institution_ids":["https://openalex.org/I40036882"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102759207","display_name":"Michael Krivelevich","orcid":null},"institutions":[{"id":"https://openalex.org/I2799411422","display_name":"Center for Discrete Mathematics and Theoretical Computer Science","ror":"https://ror.org/00k551w06","country_code":"US","type":"facility","lineage":["https://openalex.org/I102322142","https://openalex.org/I118347220","https://openalex.org/I1283103587","https://openalex.org/I1311060795","https://openalex.org/I20089843","https://openalex.org/I2799411422","https://openalex.org/I4210107353"]},{"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","US"],"is_corresponding":false,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["Department of Mathematics, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel","This research was performed in part while being with DIMACS Center, Rutgers University, Piscataway, NJ, and was supported by an IAS-DIMACS Postdoctoral Fellowship"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"This research was performed in part while being with DIMACS Center, Rutgers University, Piscataway, NJ, and was supported by an IAS-DIMACS Postdoctoral Fellowship","institution_ids":["https://openalex.org/I2799411422"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111578201"],"corresponding_institution_ids":["https://openalex.org/I40036882","https://openalex.org/I95457486"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.6653,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.61350844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9970999956130981,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9952999949455261,"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/ramseys-theorem","display_name":"Ramsey's theorem","score":0.8467675447463989},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7548923492431641},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7496968507766724},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5861652493476868},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5764592885971069},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5052435994148254},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4916134476661682},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.41769590973854065},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4175187051296234},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4164450168609619}],"concepts":[{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.8467675447463989},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7548923492431641},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7496968507766724},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5861652493476868},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5764592885971069},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5052435994148254},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4916134476661682},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.41769590973854065},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4175187051296234},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4164450168609619},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/1098-2418(200008)17:1<1::aid-rsa1>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1098-2418(200008)17:1<1::aid-rsa1>3.0.co;2-4","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.21.9833","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.9833","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/30.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1559492868","https://openalex.org/W1971734630","https://openalex.org/W1971994465","https://openalex.org/W1974683938","https://openalex.org/W1988522098","https://openalex.org/W2058619174","https://openalex.org/W2067023564","https://openalex.org/W2115730400","https://openalex.org/W2912057363","https://openalex.org/W4236734508"],"related_works":["https://openalex.org/W2963272825","https://openalex.org/W2036810061","https://openalex.org/W4318195686","https://openalex.org/W2975999359","https://openalex.org/W2149859310","https://openalex.org/W2174974817","https://openalex.org/W2069040548","https://openalex.org/W4226136150","https://openalex.org/W4322708012","https://openalex.org/W1629966990"],"abstract_inverted_index":{"In":[0],"a":[1,23,29,50,63,74,129,137],"series":[2],"of":[3,15,18,41,53,62,185],"papers":[4],"culminating":[5],"in":[6,45,57,113],"[11]":[7],"R\u00f6dl,":[8],"Ruci\u0144ski":[9],"and":[10,66,70,121],"others":[11],"study":[12],"the":[13,35,60,93,116,151,156,183,186],"thresholds":[14],"Ramsey":[16,89,152],"properties":[17],"random":[19,30,75,138],"graphs":[20],"i.e.":[21],"for":[22,38,134],"given":[24],"graph":[25,31,76,139],"H,":[26],"when":[27,92,155],"does":[28,85,148],"almost":[32,83,101,146,164],"surely":[33,84,102,147,165],"have":[34,87,150],"property":[36],"that":[37,73,112,133],"every":[39,135],"coloring":[40],"its":[42],"vertices":[43],"(edges)":[44],"r":[46],"colors":[47],"there":[48],"exists":[49,128],"monochromatic":[51],"copy":[52],"H.":[54],"They":[55],"prove":[56],"many":[58],"cases":[59],"existence":[61,173],"function":[64,130,187],"p(n,H)":[65],"two":[67],"constants":[68],"c(H)":[69],"C(H)":[71],"such":[72,132],"with":[77,140],"edge":[78,94,141,157],"probability":[79,95,142,158],"at":[80,97,160],"most":[81],"cp":[82],"not":[86,149],"this":[88,104,167,170],"property,":[90,153],"whereas":[91,154],"is":[96,159,171],"least":[98,161],"Cp":[99],"it":[100,163],"has":[103,166],"property.":[105,168],"We":[106],"complement":[107],"their":[108],"results":[109],"by":[110],"showing":[111],"certain":[114],"cases,":[115],"multiplicative":[117],"gap":[118],"between":[119],"upper":[120],"lower":[122],"bound":[123],"can":[124],"be":[125],"closed:":[126],"There":[127],"p(n)":[131],"\u03b5,":[136],"less":[143],"than":[144],"(1\u2212\u03b5)p":[145],"(1+\u03b5)p":[162],"However,":[169],"an":[172],"result":[174],"only,":[175],"since":[176],"our":[177],"method":[178],"yields":[179],"no":[180],"information":[181],"about":[182],"value":[184],"p(n).":[188],"\u00a9":[189],"2000":[190,201],"John":[191],"Wiley":[192],"&":[193],"Sons,":[194],"Inc.":[195],"Random":[196],"Struct.":[197],"Alg.,":[198],"17:":[199],"1\u201319,":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
