{"id":"https://openalex.org/W2108315536","doi":"https://doi.org/10.1017/s0963548310000532","title":"3-Connected Cores In Random Planar Graphs","display_name":"3-Connected Cores In Random Planar Graphs","publication_year":2011,"publication_date":"2011-01-24","ids":{"openalex":"https://openalex.org/W2108315536","doi":"https://doi.org/10.1017/s0963548310000532","mag":"2108315536"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548310000532","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548310000532","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5026047559","display_name":"Nikolaos Fountoulakis","orcid":"https://orcid.org/0000-0002-5751-7575"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"NIKOLAOS FOUNTOULAKIS","raw_affiliation_strings":["Max-Planck-Institute for Informatics, Campus E.1 4, D-66123 Saarbr\u00fccken, Germany (e-mail:","Max-planck-institute for informatics, campus e.1 4, d-66123 saarbr\u00fccken, germany (e-mail: fountoul@mpi-inf.mpg.de, kpanagio@mpi-inf.mpg.de)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institute for Informatics, Campus E.1 4, D-66123 Saarbr\u00fccken, Germany (e-mail:","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Max-planck-institute for informatics, campus e.1 4, d-66123 saarbr\u00fccken, germany (e-mail: fountoul@mpi-inf.mpg.de, kpanagio@mpi-inf.mpg.de)#TAB#","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075970062","display_name":"\u039a\u03c9\u03bd\u03c3\u03c4\u03b1\u03bd\u03c4\u03af\u03bd\u03bf\u03c2 \u03a0\u03b1\u03bd\u03b1\u03b3\u03b9\u03ce\u03c4\u03bf\u03c5","orcid":"https://orcid.org/0000-0002-9258-6082"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"KONSTANTINOS PANAGIOTOU","raw_affiliation_strings":["Max-Planck-Institute for Informatics, Campus E.1 4, D-66123 Saarbr\u00fccken, Germany (e-mail:","Max-planck-institute for informatics, campus e.1 4, d-66123 saarbr\u00fccken, germany (e-mail: fountoul@mpi-inf.mpg.de, kpanagio@mpi-inf.mpg.de)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institute for Informatics, Campus E.1 4, D-66123 Saarbr\u00fccken, Germany (e-mail:","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Max-planck-institute for informatics, campus e.1 4, d-66123 saarbr\u00fccken, germany (e-mail: fountoul@mpi-inf.mpg.de, kpanagio@mpi-inf.mpg.de)#TAB#","institution_ids":["https://openalex.org/I4210109712"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210109712"],"apc_list":null,"apc_paid":null,"fwci":7.3458,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.96046827,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"3","first_page":"381","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9979000091552734,"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":0.9940000176429749,"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":0.7553894519805908},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6375173330307007},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.598321795463562},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.576545000076294},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5095837116241455},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4712282419204712},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.45755162835121155},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4450233280658722},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.4225865602493286},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.4166174530982971},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.36964213848114014},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.31187325716018677},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23000577092170715}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7553894519805908},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6375173330307007},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.598321795463562},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.576545000076294},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5095837116241455},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4712282419204712},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.45755162835121155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4450233280658722},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.4225865602493286},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.4166174530982971},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36964213848114014},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.31187325716018677},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23000577092170715},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0963548310000532","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548310000532","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.313.1702","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.313.1702","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0907.2326v1.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:618746","is_oa":false,"landing_page_url":"http://edoc.mpg.de/618746","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability &amp; Computing, v.20, 381-412 (2011)","raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/fdee537b-392d-4f44-b293-048bca8a3c4d","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/fdee537b-392d-4f44-b293-048bca8a3c4d","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fountoulakis, N & Panagiotou, K 2011, '3-Connected Cores In Random Planar Graphs', Combinatorics, Probability and Computing, vol. 20, no. 03, pp. 381-412. https://doi.org/10.1017/S0963548310000532","raw_type":"article"},{"id":"pmh:oai:pure.mpg.de:item_1562341","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0010-11D0-C","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability & Computing","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W151079317","https://openalex.org/W186403072","https://openalex.org/W656781005","https://openalex.org/W1504925519","https://openalex.org/W1589957632","https://openalex.org/W1933831472","https://openalex.org/W1970541826","https://openalex.org/W1982202832","https://openalex.org/W2018165282","https://openalex.org/W2080171801","https://openalex.org/W2099787737","https://openalex.org/W2123221405","https://openalex.org/W2134147092","https://openalex.org/W2340541605","https://openalex.org/W2478722229","https://openalex.org/W3144881883","https://openalex.org/W4246059520","https://openalex.org/W4252334863"],"related_works":["https://openalex.org/W603403972","https://openalex.org/W1544821268","https://openalex.org/W2133160845","https://openalex.org/W1578113210","https://openalex.org/W1554245510","https://openalex.org/W2061237693","https://openalex.org/W2239518402","https://openalex.org/W1776247756","https://openalex.org/W2564891670","https://openalex.org/W2442922754"],"abstract_inverted_index":{"The":[0],"study":[1,45],"of":[2,6,18,47,64,72,110,134,196,229,231],"the":[3,62,70,135,166,208,213,227],"structural":[4,53],"properties":[5,46],"large":[7],"random":[8,29,48,65,90,105,246],"planar":[9,30,67,248],"graphs":[10,49,68,92],"has":[11],"become":[12],"in":[13,21,146,255],"recent":[14],"years":[15],"a":[16,28,86,100,107,142,154,240,245],"field":[17],"intense":[19],"research":[20],"computer":[22],"science":[23],"and":[24,35,173,220,236,262],"discrete":[25],"mathematics.":[26],"Nowadays,":[27],"graph":[31,101,249],"is":[32,99,141,153],"an":[33],"important":[34],"challenging":[36],"model":[37],"for":[38,226],"evaluating":[39],"methods":[40],"that":[41,117,150,165,211,244],"are":[42],"developed":[43],"to":[44,131,215,251],"from":[50,93,106],"classes":[51],"with":[52,118],"side":[54],"constraints.":[55],"In":[56,82],"this":[57],"paper":[58],"we":[59,78,84,115,206,242],"focus":[60],"on":[61],"structure":[63],"2-connected":[66],"regarding":[69,89],"sizes":[71,233],"their":[73],"3-connected":[74],"building":[75],"blocks,":[76],"which":[77,216],"call":[79],"cores":[80,195,230],".":[81,238,260,261],"fact,":[83],"prove":[85],"general":[87],"theorem":[88],"biconnected":[91,112,247],"various":[94],"classes.":[95],"If":[96],"B":[97,128,147,197,217],"n":[98,125,129,148,180,198,202,218,237],"drawn":[102],"uniformly":[103],"at":[104,178],"suitable":[108],"class":[109],"labelled":[111],"graphs,":[113],"then":[114],"show":[116],"probability":[119],"1":[120,163,235],"\u2212":[121],"o":[122],"(1)":[123],"as":[124],"\u2192":[126],"\u221e,":[127],"belongs":[130,250],"exactly":[132],"one":[133],"following":[136],"categories:":[137],"(i)":[138],"either":[139],"there":[140,152],"unique":[143],"giant":[144],"core":[145,168,176],",":[149],"is,":[151],"0":[155,184],"&lt;":[156,162,185,190],"c":[157,159,257],"=":[158,187,258,264],"(":[160],")":[161,189,203],"such":[164],"largest":[167],"contains":[169,177],"~":[170],"cn":[171],"vertices,":[172,182],"every":[174],"other":[175],"most":[179],"\u03b1":[181,186,263],"where":[183,254],"\u03b1(":[188],"1;":[191],"(ii)":[192],"or":[193],"all":[194,232],"contain":[199],"O":[200],"(log":[201],"vertices.":[204],"Moreover,":[205],"find":[207],"critical":[209],"condition":[210],"determines":[212],"category":[214,252],"belongs,":[219],"also":[221],"provide":[222],"sharp":[223],"concentration":[224],"results":[225],"counts":[228],"between":[234],"As":[239],"corollary,":[241],"obtain":[243],"(i),":[253],"particular":[256],"0.765.":[259],"2/3.":[265]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
