{"id":"https://openalex.org/W2002667707","doi":"https://doi.org/10.1017/s0963548312000181","title":"Perfect Graphs of Fixed Density: Counting and Homogeneous Sets","display_name":"Perfect Graphs of Fixed Density: Counting and Homogeneous Sets","publication_year":2012,"publication_date":"2012-05-14","ids":{"openalex":"https://openalex.org/W2002667707","doi":"https://doi.org/10.1017/s0963548312000181","mag":"2002667707"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548312000181","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000181","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/A5063881498","display_name":"Julia B\u00f6ttcher","orcid":"https://orcid.org/0000-0002-4104-3635"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"JULIA B\u00d6TTCHER","raw_affiliation_strings":["Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK (e-mail:","Department of mathematics, london school of economics, houghton street, london wc2a 2ae, uk (e-mail: j.boettcher@lse.ac.uk)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK (e-mail:","institution_ids":["https://openalex.org/I909854389"]},{"raw_affiliation_string":"Department of mathematics, london school of economics, houghton street, london wc2a 2ae, uk (e-mail: j.boettcher@lse.ac.uk)#TAB#","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026270025","display_name":"Anusch Taraz","orcid":"https://orcid.org/0000-0003-3646-3683"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"ANUSCH TARAZ","raw_affiliation_strings":["Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85747 Garching bei M\u00fcnchen, Germany (e-mail:","Zentrum mathematik, technische universit\u00e4t m\u00fcnchen, boltzmannstra\u03b2e 3, d-85747 garching bei m\u00fcnchen, germany (e-mail: taraz@ma.tum.de, wuerfl@ma.tum.de)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85747 Garching bei M\u00fcnchen, Germany (e-mail:","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Zentrum mathematik, technische universit\u00e4t m\u00fcnchen, boltzmannstra\u03b2e 3, d-85747 garching bei m\u00fcnchen, germany (e-mail: taraz@ma.tum.de, wuerfl@ma.tum.de)#TAB#","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050811018","display_name":"Andreas W\u00fcrfl","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"ANDREAS W\u00dcRFL","raw_affiliation_strings":["Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85747 Garching bei M\u00fcnchen, Germany (e-mail:","Zentrum mathematik, technische universit\u00e4t m\u00fcnchen, boltzmannstra\u03b2e 3, d-85747 garching bei m\u00fcnchen, germany (e-mail: taraz@ma.tum.de, wuerfl@ma.tum.de)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstra\u00dfe 3, D-85747 Garching bei M\u00fcnchen, Germany (e-mail:","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Zentrum mathematik, technische universit\u00e4t m\u00fcnchen, boltzmannstra\u03b2e 3, d-85747 garching bei m\u00fcnchen, germany (e-mail: taraz@ma.tum.de, wuerfl@ma.tum.de)#TAB#","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08980007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"5","first_page":"661","last_page":"682"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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/T11476","display_name":"Graph theory and applications","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7588354349136353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7310802936553955},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6628271341323853},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6092249751091003},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.51693195104599},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4799528419971466},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4724298417568207},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3397112488746643},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07239904999732971}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7588354349136353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7310802936553955},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6628271341323853},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6092249751091003},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.51693195104599},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4799528419971466},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4724298417568207},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3397112488746643},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07239904999732971}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548312000181","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000181","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:researchonline.lse.ac.uk:45495","is_oa":false,"landing_page_url":"https://orcid.org/0000-0002-4104-3635>,","pdf_url":null,"source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:eprints.lse.ac.uk:45495","is_oa":false,"landing_page_url":"http://eprints.lse.ac.uk/45495/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W155336174","https://openalex.org/W788200807","https://openalex.org/W1022649828","https://openalex.org/W1487047352","https://openalex.org/W1540243329","https://openalex.org/W1568934558","https://openalex.org/W1973199140","https://openalex.org/W1977647916","https://openalex.org/W1985538939","https://openalex.org/W1991488719","https://openalex.org/W1993010909","https://openalex.org/W2007044730","https://openalex.org/W2018242275","https://openalex.org/W2038080222","https://openalex.org/W2079092774","https://openalex.org/W2079843645","https://openalex.org/W2093276208","https://openalex.org/W2103229001","https://openalex.org/W2106491342","https://openalex.org/W2111007781","https://openalex.org/W2137272630","https://openalex.org/W2145702572","https://openalex.org/W2479487043","https://openalex.org/W2490672683","https://openalex.org/W2501518369","https://openalex.org/W3008660429","https://openalex.org/W4229606576","https://openalex.org/W4229956213"],"related_works":["https://openalex.org/W1719252778","https://openalex.org/W2031098440","https://openalex.org/W4307385446","https://openalex.org/W2466894780","https://openalex.org/W3092119098","https://openalex.org/W2003008160","https://openalex.org/W2381713449","https://openalex.org/W2731724293","https://openalex.org/W2904724461","https://openalex.org/W2999858140"],"abstract_inverted_index":{"For":[0],"c":[1,15],"\u2208":[2],"(0,1)":[3],"let":[4,17],"n(c)":[5,18,56],"denote":[6,19],"the":[7,20,40],"set":[8,21],"of":[9,22,60],"n-vertex":[10,23],"perfect":[11],"graphs":[12,24,54],"with":[13,29,35],"density":[14,30],"and":[16,28,70],"without":[25],"induced":[26],"C5":[27],"c.":[31],"We":[32],"show":[33],"that":[34,51],"otherwise,":[36],"where":[37],"H":[38],"is":[39],"binary":[41],"entropy":[42],"function.":[43],"Further,":[44],"we":[45],"use":[46],"this":[47],"result":[48],"to":[49],"deduce":[50],"almost":[52],"all":[53],"in":[55],"have":[57],"homogeneous":[58],"sets":[59],"linear":[61],"size.":[62],"This":[63],"answers":[64],"a":[65],"question":[66],"raised":[67],"by":[68],"Loebl":[69],"co-workers.":[71]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}