{"id":"https://openalex.org/W2606486516","doi":"https://doi.org/10.37236/6639","title":"$\\delta$-Connectivity in Random Lifts of Graphs","display_name":"$\\delta$-Connectivity in Random Lifts of Graphs","publication_year":2017,"publication_date":"2017-03-17","ids":{"openalex":"https://openalex.org/W2606486516","doi":"https://doi.org/10.37236/6639","mag":"2606486516"},"language":"en","primary_location":{"id":"doi:10.37236/6639","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6639","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6639","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078443823","display_name":"Shashwat Silas","orcid":"https://orcid.org/0000-0002-1742-7137"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shashwat Silas","raw_affiliation_strings":["Stanford University"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078443823"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07121796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9990000128746033,"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":0.9990000128746033,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9969000220298767,"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/mathematics","display_name":"Mathematics","score":0.8724561929702759},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8604675531387329},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.7799969911575317},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.600302517414093},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5199707746505737},{"id":"https://openalex.org/keywords/delta","display_name":"Delta","score":0.4659724235534668},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4379939138889313},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42327970266342163},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06773334741592407}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8724561929702759},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8604675531387329},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.7799969911575317},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.600302517414093},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5199707746505737},{"id":"https://openalex.org/C5072461","wikidata":"https://www.wikidata.org/wiki/Q49506","display_name":"Delta","level":2,"score":0.4659724235534668},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4379939138889313},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42327970266342163},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06773334741592407},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/6639","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6639","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/6639","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6639","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4221046490","https://openalex.org/W4297616267","https://openalex.org/W2502651140","https://openalex.org/W3195406774","https://openalex.org/W4297615481","https://openalex.org/W4297616317","https://openalex.org/W3111070561","https://openalex.org/W4239373651","https://openalex.org/W2414832939","https://openalex.org/W4297616379"],"abstract_inverted_index":{"Amit":[0],"and":[1,23,50,77,106,111],"Linial":[2],"have":[3],"shown":[4],"that":[5,63,89,114,145],"a":[6,10,32,41,44,48,51,98,123,127,138,146,149,162],"random":[7,45,115,135,157],"lift":[8,105],"of":[9,27,34,37,47,55,100,103,109,134,148,152,166,174],"connected":[11],"graph":[12,49],"with":[13,82],"minimum":[14],"degree":[15,36,102],"$\\delta\\ge3$":[16],"is":[17,66,79,159],"asymptotically":[18],"almost":[19],"surely":[20],"(a.a.s.)":[21],"$\\delta$-connected":[22],"mentioned":[24],"the":[25,35,38,56,101,104,107,131,143,170,175],"problem":[26],"estimating":[28],"this":[29,64,86],"probability":[30,65,144],"as":[31,97],"function":[33,99],"lift.":[39],"Using":[40],"connection":[42],"between":[43],"$n$-lift":[46],"randomly":[52],"generated":[53,155],"subgroup":[54,147],"symmetric":[57,153,176],"group":[58],"on":[59,130],"$n$-elements,":[60],"we":[61,141],"show":[62,88],"at":[67],"least":[68],"$1":[69],"-":[70],"O\\left(\\frac{1}{n^{\\gamma(\\delta)}}\\right)$":[71],"where":[72],"$\\gamma(\\delta)>0$":[73],"for":[74,172],"$\\delta\\ge":[75],"5$":[76],"it":[78],"strictly":[80],"increasing":[81],"$\\delta$.":[83],"We":[84,120],"extend":[85],"to":[87,94],"one":[90],"may":[91],"allow":[92],"$\\delta$":[93],"grow":[95],"slowly":[96],"number":[108],"vertices":[110],"still":[112],"obtain":[113],"lifts":[116],"are":[117],"a.a.s.":[118],"$\\delta$-connected.":[119],"also":[121],"simplify":[122],"later":[124],"result":[125,165],"showing":[126],"lower":[128],"bound":[129],"edge":[132],"expansion":[133],"lifts.":[136],"On":[137],"related":[139],"note,":[140],"calculate":[142],"wreath":[150],"product":[151],"groups":[154],"by":[156],"generators":[158],"transitive,":[160],"extending":[161],"well":[163],"known":[164],"Dixon":[167],"which":[168],"covers":[169],"case":[171],"subgroups":[173],"group.":[177]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}