{"id":"https://openalex.org/W137750514","doi":"https://doi.org/10.1017/s0963548314000303","title":"Asymptotic Properties of Some Minor-Closed Classes of Graphs","display_name":"Asymptotic Properties of Some Minor-Closed Classes of Graphs","publication_year":2014,"publication_date":"2014-07-09","ids":{"openalex":"https://openalex.org/W137750514","doi":"https://doi.org/10.1017/s0963548314000303","mag":"137750514"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548314000303","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000303","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1303.3836","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014744803","display_name":"Mireille Bousquet\u2010M\u00e9lou","orcid":"https://orcid.org/0000-0002-2863-8300"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"MIREILLE BOUSQUET-M\u00c9LOU","raw_affiliation_strings":["MBM: CNRS, LaBRI, UMR 5800, Universit\u00e9 de Bordeaux, 351 Cours de la Lib\u00e9ration, 33405 Talence Cedex, France (e-mail:"],"affiliations":[{"raw_affiliation_string":"MBM: CNRS, LaBRI, UMR 5800, Universit\u00e9 de Bordeaux, 351 Cours de la Lib\u00e9ration, 33405 Talence Cedex, France (e-mail:","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I1294671590","https://openalex.org/I4210142254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024260113","display_name":"Kerstin Weller","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"KERSTIN WELLER","raw_affiliation_strings":["KW: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, UK (e-mail:"],"affiliations":[{"raw_affiliation_string":"KW: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, UK (e-mail:","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014744803"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254"],"apc_list":null,"apc_paid":null,"fwci":1.6691,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.77601614,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"5","first_page":"749","last_page":"795"},"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":0.7193999886512756,"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":0.7193999886512756,"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/T11476","display_name":"Graph theory and applications","score":0.09000000357627869,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.08579999953508377,"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":0.6913349628448486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6879154443740845},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.6114916205406189},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.509584903717041},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5031132102012634},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4951228201389313},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47775736451148987},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.4732288122177124},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.4504458010196686},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4496774673461914},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44395187497138977},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.4379655122756958},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4371248483657837},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4271831810474396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16262221336364746},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08368590474128723},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07187023758888245},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.07075458765029907}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6913349628448486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6879154443740845},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.6114916205406189},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.509584903717041},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5031132102012634},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4951228201389313},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47775736451148987},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.4732288122177124},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.4504458010196686},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4496774673461914},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44395187497138977},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.4379655122756958},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4371248483657837},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4271831810474396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16262221336364746},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08368590474128723},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07187023758888245},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.07075458765029907},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548314000303","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000303","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:arXiv.org:1303.3836","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.3836","pdf_url":"https://arxiv.org/pdf/1303.3836","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1303.3836","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.3836","pdf_url":"https://arxiv.org/pdf/1303.3836","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W186403072","https://openalex.org/W196531003","https://openalex.org/W1258338664","https://openalex.org/W1489554514","https://openalex.org/W1600388690","https://openalex.org/W1981036944","https://openalex.org/W1982202832","https://openalex.org/W1997875704","https://openalex.org/W2000910910","https://openalex.org/W2045390532","https://openalex.org/W2049665706","https://openalex.org/W2054113620","https://openalex.org/W2055758813","https://openalex.org/W2061450212","https://openalex.org/W2065436557","https://openalex.org/W2067079496","https://openalex.org/W2068728923","https://openalex.org/W2071275210","https://openalex.org/W2079265093","https://openalex.org/W2099787737","https://openalex.org/W2113232101","https://openalex.org/W2121373282","https://openalex.org/W2134147092","https://openalex.org/W2142101067","https://openalex.org/W2153847184","https://openalex.org/W2158374239","https://openalex.org/W2168140459","https://openalex.org/W2596372383","https://openalex.org/W3103129687"],"related_works":["https://openalex.org/W2368619281","https://openalex.org/W2377143628","https://openalex.org/W2355995962","https://openalex.org/W2290279467","https://openalex.org/W4387641633","https://openalex.org/W2023655621","https://openalex.org/W2950527329","https://openalex.org/W1534465152","https://openalex.org/W2010051735","https://openalex.org/W2887091383"],"abstract_inverted_index":{"Let":[0],"${\\cal":[1,12,28,40,85,128],"A}$":[2,29,86,129],"be":[3,14,97],"a":[4,15,81,138,142,152,181],"minor-closed":[5,145],"class":[6],"of":[7,23,27,60,83,111,115,127,144,147,166],"labelled":[8],"graphs,":[9],"and":[10,62,90,176,178],"let":[11],"G}_{n}$":[13,41],"random":[16],"graph":[17],"sampled":[18],"uniformly":[19],"from":[20,100],"the":[21,37,58,101,109,112,116,164,167],"set":[22],"n":[24,32],"-vertex":[25],"graphs":[26,126],".":[30,130],"When":[31],"is":[33,36,42,52],"large,":[34],"what":[35],"probability":[38],"that":[39,92,123,154],"connected?":[43],"How":[44,50],"many":[45],"components":[46],"does":[47],"it":[48],"have?":[49],"large":[51],"its":[53],"biggest":[54],"component?":[55],"Thanks":[56],"to":[57],"work":[59],"McDiarmid":[61],"his":[63],"collaborators,":[64],"these":[65],"questions":[66],"are":[67,74],"now":[68],"solved":[69],"when":[70],"all":[71],"excluded":[72],"minors":[73],"2-connected.":[75],"Using":[76],"exact":[77],"enumeration,":[78],"we":[79,150],"study":[80],"collection":[82],"classes":[84,146],"excluding":[87],"non-2-connected":[88],"minors,":[89],"show":[91],"their":[93],"asymptotic":[94],"behaviour":[95,105],"may":[96],"rather":[98],"different":[99],"2-connected":[102],"case.":[103],"This":[104],"largely":[106],"depends":[107],"on":[108],"nature":[110],"dominant":[113],"singularity":[114],"generating":[117],"function":[118],"C":[119],"(":[120],"z":[121],")":[122],"counts":[124],"connected":[125],"We":[131],"classify":[132],"our":[133],"examples":[134],"accordingly,":[135],"thus":[136],"taking":[137],"first":[139],"step":[140],"towards":[141],"classification":[143],"graphs.":[148],"Furthermore,":[149],"investigate":[151],"parameter":[153],"has":[155],"not":[156],"received":[157],"any":[158],"attention":[159],"in":[160],"this":[161],"context":[162],"yet:":[163],"size":[165],"root":[168],"component.":[169],"It":[170],"follows":[171],"non-Gaussian":[172],"limit":[173],"laws":[174],"(Beta":[175],"Gamma),":[177],"clearly":[179],"merits":[180],"systematic":[182],"investigation.":[183]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-03T08:47:05.690250","created_date":"2025-10-10T00:00:00"}