{"id":"https://openalex.org/W2012759587","doi":"https://doi.org/10.1002/rsa.3240050503","title":"On the diameter and radius of randon subgraphs of the cube","display_name":"On the diameter and radius of randon subgraphs of the cube","publication_year":1994,"publication_date":"1994-12-01","ids":{"openalex":"https://openalex.org/W2012759587","doi":"https://doi.org/10.1002/rsa.3240050503","mag":"2012759587"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240050503","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240050503","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 &amp; Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://doi.org/10.1002/rsa.3240050503","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111762239","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"]}],"countries":["GB"],"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, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"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 Sa\u0303o Paulo, Caixa Postal 20570, 01452\u2013990 Sa\u0303o Paulo, SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matema\u0301tica e Estati\u0301stica, Universidade de Sa\u0303o Paulo, Caixa Postal 20570, 01452\u2013990 Sa\u0303o 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. \u0141uczak","raw_affiliation_strings":["Mathematical insitute of the Polish Academy of Sciences, Poznan\u0301, Poland","On leave from the Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, Poznan\u0301, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical insitute of the Polish Academy of Sciences, Poznan\u0301, 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, Poznan\u0301, Poland","institution_ids":["https://openalex.org/I59411706"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":1.1597,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.73018754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":"5","first_page":"627","last_page":"648"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9995999932289124,"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":0.9995999932289124,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9927999973297119,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8510600328445435},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5577245950698853},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5004477500915527},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4585956633090973},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3887467384338379}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8510600328445435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5577245950698853},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5004477500915527},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4585956633090973},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3887467384338379},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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":2,"locations":[{"id":"doi:10.1002/rsa.3240050503","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240050503","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 &amp; Algorithms","raw_type":"journal-article"},{"id":"pmh:002947094","is_oa":true,"landing_page_url":"http://doi.org/10.1002/rsa.3240050503","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:002947094","is_oa":true,"landing_page_url":"http://doi.org/10.1002/rsa.3240050503","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":"publishedVersion","is_accepted":true,"is_published":true,"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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W23862387","https://openalex.org/W54900758","https://openalex.org/W128463146","https://openalex.org/W1992324268","https://openalex.org/W1996527251","https://openalex.org/W2003745268","https://openalex.org/W2005443809","https://openalex.org/W2026620883","https://openalex.org/W2067049861","https://openalex.org/W2067667206","https://openalex.org/W2075997628","https://openalex.org/W2905110430","https://openalex.org/W4254836771"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"n":[2,6,17,35,40,45,52,59,74,85,108,179,193,224],"\u2010dimensional":[3],"cube":[4],"Q":[5,34,51,58,62,65,73,77,84,91,96,107,111,122,151,155,207,246],"is":[7,30,79,93,169,210],"the":[8,13,55,100,127,131,144,204,222,234,239],"graph":[9],"whose":[10],"vertices":[11,21],"are":[12,228],"subsets":[14],"of":[15,57,83,86,103,106,130,133,154,206,238,245],"{1,\u2026":[16],"},":[18],"with":[19],"two":[20],"adjacent":[22],"if":[23,26],"and":[24,38,90,168,188,236],"only":[25],"their":[27],"symmetric":[28],"difference":[29],"a":[31,71,80],"singleton.":[32],"Clearly":[33],"has":[36],"diameter":[37,145,235],"radious":[39],".":[41,60,140,199,225],"Write":[42],"M":[43,69,253],"=":[44,48,63,120,148,192,215,251],"2":[46],"n\u20101":[47],"e":[49],"(":[50,64,117,150],")":[53,67,119,125,153],"for":[54,182,194,213,249],"size":[56,87],"Let":[61,115],"t":[66,78,88,92,97,112,116,147,152,156,165,174,183,186,190,195,197,208,214,216,247,250],"o":[68],"be":[70,126],"random":[72,101],"\u2010process.":[75],"Thus":[76],"spanning":[81],"subgraph":[82],",":[89,114,176,191,209,218,248],"obtained":[94],"from":[95,230],"\u20131":[98,113],"by":[99],"addition":[102],"an":[104],"edge":[105],"not":[109],"in":[110,157],"k":[118,124,139],"\u03c4(":[121],";\u03b4\u2a7e":[123],"hitting":[128],"time":[129,173],"property":[132],"having":[134],"minimal":[135],"degree":[136],"at":[137,172],"least":[138],"We":[141,200],"show":[142,202],"that":[143,203],"d":[146,164,189],"diam":[149],"almost":[158,240],"every":[159],"Q\u0303":[160],"behaves":[161],"as":[162],"follows:":[163],"starts":[166],"infinite":[167],"first":[170,211],"finite":[171,212],"(1)":[175,184,217],"it":[177,220],"equals":[178],"+":[180],"1":[181],"\u2a7d":[185],"(2)":[187,198],"\u2a7e":[196],"also":[201],"radius":[205,237],"when":[219],"assumes":[221],"value":[223],"These":[226],"results":[227],"deduced":[229],"detailed":[231],"theorems":[232],"concerning":[233],"surely":[241],"unique":[242],"largest":[243],"component":[244],"\u03a9(":[252],").":[254],"\u00a9":[255],"1994":[256],"John":[257],"Wiley":[258],"&amp;":[259],"Sons,":[260],"Inc.":[261]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
