{"id":"https://openalex.org/W2138204011","doi":"https://doi.org/10.37236/2793","title":"Random Graphs from a Weighted Minor-Closed Class","display_name":"Random Graphs from a Weighted Minor-Closed Class","publication_year":2013,"publication_date":"2013-06-07","ids":{"openalex":"https://openalex.org/W2138204011","doi":"https://doi.org/10.37236/2793","mag":"2138204011"},"language":"en","primary_location":{"id":"doi:10.37236/2793","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2793","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p52/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p52/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111437501","display_name":"Colin McDiarmid","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":true,"raw_author_name":"Colin McDiarmid","raw_affiliation_strings":["University of Oxford, UK","University of Oxford, UK,"],"affiliations":[{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Oxford, UK,","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111437501"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":1.1192,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80408685,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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":0.9973999857902527,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9958999752998352,"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":0.7435858845710754},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.7240731716156006},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.6573096513748169},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6405851244926453},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6106418967247009},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.5930876135826111},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.5879499912261963},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5516060590744019},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.550478994846344},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.4962971806526184},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.4840252101421356},{"id":"https://openalex.org/keywords/modular-decomposition","display_name":"Modular decomposition","score":0.4704137146472931},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.45069509744644165},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4314113259315491},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4209333658218384},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.25679337978363037},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1773836612701416}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7435858845710754},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.7240731716156006},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.6573096513748169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6405851244926453},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6106418967247009},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.5930876135826111},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.5879499912261963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5516060590744019},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.550478994846344},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.4962971806526184},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.4840252101421356},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.4704137146472931},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.45069509744644165},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4314113259315491},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4209333658218384},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.25679337978363037},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1773836612701416}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/2793","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2793","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p52/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1210.2701","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.2701","pdf_url":"https://arxiv.org/pdf/1210.2701","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":"","raw_type":"text"},{"id":"mag:2138204011","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1210.2701","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:ora.ox.ac.uk:uuid:d9126a3f-7bb1-4aab-8038-cef3e91bc9d2","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:d9126a3f-7bb1-4aab-8038-cef3e91bc9d2","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"},{"id":"doi:10.48550/arxiv.1210.2701","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1210.2701","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/2793","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2793","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p52/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2138204011.pdf","grobid_xml":"https://content.openalex.org/works/W2138204011.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W108214179","https://openalex.org/W151079317","https://openalex.org/W599250420","https://openalex.org/W1258338664","https://openalex.org/W1554192949","https://openalex.org/W1574394872","https://openalex.org/W1589957632","https://openalex.org/W1600388690","https://openalex.org/W1649656253","https://openalex.org/W1691710745","https://openalex.org/W1970541826","https://openalex.org/W1981036944","https://openalex.org/W1999694424","https://openalex.org/W2001253902","https://openalex.org/W2007080218","https://openalex.org/W2014744271","https://openalex.org/W2018165282","https://openalex.org/W2021469741","https://openalex.org/W2024781825","https://openalex.org/W2029630058","https://openalex.org/W2032192593","https://openalex.org/W2033652300","https://openalex.org/W2042502099","https://openalex.org/W2043083610","https://openalex.org/W2049665706","https://openalex.org/W2052068320","https://openalex.org/W2057857650","https://openalex.org/W2058647687","https://openalex.org/W2058824702","https://openalex.org/W2062179655","https://openalex.org/W2065436557","https://openalex.org/W2073593086","https://openalex.org/W2078000356","https://openalex.org/W2108315536","https://openalex.org/W2113232101","https://openalex.org/W2117621804","https://openalex.org/W2123221405","https://openalex.org/W2134147092","https://openalex.org/W2140395242","https://openalex.org/W2153980238","https://openalex.org/W2158374239","https://openalex.org/W2252330517","https://openalex.org/W2601965285","https://openalex.org/W3102272889","https://openalex.org/W3103129687","https://openalex.org/W3138122991","https://openalex.org/W6628819890","https://openalex.org/W6635243753","https://openalex.org/W6638119950","https://openalex.org/W6642686841","https://openalex.org/W6663056073","https://openalex.org/W6678043570","https://openalex.org/W6680167966","https://openalex.org/W6680938120","https://openalex.org/W6685186986","https://openalex.org/W6721489647","https://openalex.org/W6728073142","https://openalex.org/W6767907350","https://openalex.org/W6786186065"],"related_works":["https://openalex.org/W2962827126","https://openalex.org/W1971728216","https://openalex.org/W2252330517","https://openalex.org/W2099787737","https://openalex.org/W2758407290","https://openalex.org/W1997570254","https://openalex.org/W2141937899","https://openalex.org/W1684832175","https://openalex.org/W2031317693","https://openalex.org/W2163069624","https://openalex.org/W3010302700","https://openalex.org/W2112212574","https://openalex.org/W3130470475","https://openalex.org/W2044936155","https://openalex.org/W2783791424","https://openalex.org/W1600388690","https://openalex.org/W2046560739","https://openalex.org/W2042732675","https://openalex.org/W3011227702","https://openalex.org/W2192488761"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"much":[3],"recent":[4],"interest":[5],"in":[6,15,123],"random":[7,43,107,112,145],"graphs":[8,14,44,60,69,76,86,108],"sampled":[9],"uniformly":[10],"from":[11,45],"the":[12,22,73,83,111,134,141,155,162],"n-vertex":[13],"a":[16,37,46,144],"suitable":[17],"minor-closed":[18,57],"class,":[19],"such":[20,53],"as":[21,66],"class":[23,48,74,84],"of":[24,49,52,59,75,85,130,143],"all":[25,56],"planar":[26,71],"graphs.":[27],"Here":[28],"we":[29,94,150],"use":[30],"combinatorial":[31],"and":[32,70,82,99,132,149],"probabilistic":[33],"methods":[34],"to":[35,97,101,110,126,133],"investigate":[36],"more":[38],"general":[39,127],"model.":[40],"We":[41],"consider":[42],"'well-behaved'":[47],"graphs:":[50],"examples":[51],"classes":[54,58,129],"include":[55],"with":[61,87],"2-connected":[62],"excluded":[63],"minors":[64],"(such":[65],"forests,":[67],"series-parallel":[68],"graphs),":[72],"embeddable":[77],"on":[78,154],"any":[79],"given":[80],"surface,":[81],"at":[88],"most":[89],"$k$":[90],"vertex-disjoint":[91],"cycles.":[92],"Also,":[93],"give":[95,152],"weights":[96],"edges":[98],"components":[100],"specify":[102],"probabilities,":[103],"so":[104],"that":[105,118],"our":[106],"correspond":[109],"cluster":[113],"model,":[114],"appropriately":[115],"conditioned.We":[116],"find":[117],"earlier":[119],"results":[120,139,153],"extend":[121],"naturally":[122],"both":[124],"directions,":[125],"well-behaved":[128],"graphs,":[131],"weighted":[135],"framework,":[136],"for":[137,161],"example":[138],"concerning":[140],"probability":[142],"graph":[146],"being":[147],"connected;":[148],"also":[151],"2-core":[156],"which":[157],"are":[158],"new":[159],"even":[160],"uniform":[163],"(unweighted)":[164],"case.":[165]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
