{"id":"https://openalex.org/W2142886572","doi":"https://doi.org/10.1002/rsa.3240060210","title":"Connectivity properties of random subgraphs of the cube","display_name":"Connectivity properties of random subgraphs of the cube","publication_year":1995,"publication_date":"1995-03-01","ids":{"openalex":"https://openalex.org/W2142886572","doi":"https://doi.org/10.1002/rsa.3240060210","mag":"2142886572"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240060210","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060210","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":true,"oa_status":"green","oa_url":"https://doi-org.ez67.periodicos.capes.gov.br/10.1002/rsa.3240060210","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110896517","display_name":"B Bollob\u00e1s","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210153325","display_name":"Institute of Mathematical Statistics","ror":"https://ror.org/043f04882","country_code":"US","type":"other","lineage":["https://openalex.org/I4210153325"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"B. Bollob\u00e1s","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England","institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210153325"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025621521","display_name":"Yoshiharu Kohayakawa","orcid":"https://orcid.org/0000-0001-7841-157X"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Y. Kohayakawa","raw_affiliation_strings":["Instituto de Matema\u0301tica e Estati\u0301stica, Universidade de Sato Paulo, Caixa Postal 20570, 01452-990 Sato Paulo, SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matema\u0301tica e Estati\u0301stica, Universidade de Sato Paulo, Caixa Postal 20570, 01452-990 Sato Paulo, SP, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003433063","display_name":"Tomasz \u0141uczak","orcid":"https://orcid.org/0000-0002-3517-9034"},"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"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"T. Luczak","raw_affiliation_strings":["Mathematical Institute of the Polish Academy of Sciences, Pozna, Poland","On leave from the Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, Pozna, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute of the Polish Academy of Sciences, Pozna, Poland","institution_ids":["https://openalex.org/I99542240"]},{"raw_affiliation_string":"On leave from the Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, Pozna, Poland","institution_ids":["https://openalex.org/I59411706"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.27603143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"6","issue":"2-3","first_page":"221","last_page":"230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9991000294685364,"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":0.9991000294685364,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9943000078201294,"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":0.8943352103233337},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7043615579605103},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5160219669342041},{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.5026094913482666},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4831485152244568},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.41378363966941833},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.41291457414627075},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4084627032279968}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8943352103233337},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7043615579605103},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5160219669342041},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.5026094913482666},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4831485152244568},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.41378363966941833},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.41291457414627075},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4084627032279968},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/rsa.3240060210","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060210","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:002946657","is_oa":true,"landing_page_url":"https://doi-org.ez67.periodicos.capes.gov.br/10.1002/rsa.3240060210","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.9029","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.9029","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ime.usp.br/~yoshi/MSs/cube_conn/conn.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:002946657","is_oa":true,"landing_page_url":"https://doi-org.ez67.periodicos.capes.gov.br/10.1002/rsa.3240060210","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W23862387","https://openalex.org/W128463146","https://openalex.org/W1489878404","https://openalex.org/W1996527251","https://openalex.org/W2003745268","https://openalex.org/W2012759587","https://openalex.org/W2026620883","https://openalex.org/W2039803631","https://openalex.org/W2075997628","https://openalex.org/W2905110430","https://openalex.org/W4254836771"],"related_works":["https://openalex.org/W3125761283","https://openalex.org/W1976722080","https://openalex.org/W3152831473","https://openalex.org/W3092556108","https://openalex.org/W3044931971","https://openalex.org/W3008541637","https://openalex.org/W3121197002","https://openalex.org/W1971197532","https://openalex.org/W2164081328","https://openalex.org/W4301046126"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"n":[2,6,17,37,54,61,85,107,166,215,225],"\u2010dimensional":[3],"cube":[4],"Q":[5,36,60,77,84,91,96,106,110,149,160,190],"is":[7,32,38,79,93,136,165,236],"the":[8,13,57,99,122,126,147,157,188,193,230],"graph":[9,41,148,189],"whose":[10],"vertices":[11,22,202],"are":[12,23,203],"subsets":[14],"of":[15,42,59,83,86,102,105,125,128,159,200,211,233],"{1,":[16],"}":[18],"where":[19],"two":[20,199],"such":[21],"adjacent":[24],"if":[25,28],"and":[26,44,90,153],"only":[27],"their":[29],"symmetric":[30],"difference":[31],"a":[33,72,80],"singleton.":[34],"Clearly":[35],"an":[39,103],"n\u2010connected":[40],"diameter":[43,158],"radius":[45],"n.":[46],"Write":[47],"M":[48,69],"=":[49,52,65,116],"n2n":[50],"\u22121":[51],"e(Q":[53],")":[55,68],"for":[56,177,218],"size":[58,87],".":[62,112,241],"Let":[63,113],"Q\u0303":[64,74],"(Q":[66],"t":[67,78,88,92,114,145,150,161,186,191,239],"0":[70],"be":[71,121],"random":[73,100],"\u2010process.":[75],"Thus":[76],"spanning":[81],"subgraph":[82],",":[89,181,216],"obtained":[94],"from":[95],"t\u20101":[97,111],"by":[98,174,205],"addition":[101],"edge":[104],"not":[108],"in":[109,138,155],"(k)":[115,187,240],"\u03c4(Q\u0303":[117],"\u03b4":[118],"\u2267":[119],"k)":[120],"hitting":[123,231],"time":[124,144,185,232],"property":[127,196],"having":[129],"minimal":[130],"degree":[131],"at":[132,143,162,184,213],"least":[133],"k.":[134],"It":[135],"shown":[137],"[5]":[139],"that,":[140,176],"almost":[141,182,237],"surely,":[142],"(1)":[146],"becomes":[151],"connected":[152,204],"that":[154,197],"fact":[156],"this":[163,172],"point":[164],"+":[167,226],"1.":[168,227],"Here":[169],"we":[170],"generalize":[171],"result":[173],"showing":[175],"any":[178,198],"fixed":[179],"k\u22672":[180],"surely":[183,238],"acquires":[192],"extremely":[194],"strong":[195],"its":[201],"k":[206,234],"internally":[207],"vertex\u2010disjoint":[208],"paths":[209],"each":[210],"length":[212,224],"most":[214],"except":[217],"possibly":[219],"one,":[220],"which":[221],"may":[222],"have":[223],"In":[228],"particular,":[229],"\u2010connectedness":[235],"\u00a9":[242],"1995":[243],"John":[244],"Wiley":[245],"&":[246],"Sons,":[247],"Inc.":[248]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}