{"id":"https://openalex.org/W3111054536","doi":"https://doi.org/10.1017/s0963548320000577","title":"Near-perfect clique-factors in sparse pseudorandom graphs","display_name":"Near-perfect clique-factors in sparse pseudorandom graphs","publication_year":2020,"publication_date":"2020-12-11","ids":{"openalex":"https://openalex.org/W3111054536","doi":"https://doi.org/10.1017/s0963548320000577","mag":"3111054536"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548320000577","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548320000577","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":true,"oa_status":"green","oa_url":"https://doi.org/10.1017/S0963548320000577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086267413","display_name":"Jie Han","orcid":"https://orcid.org/0000-0002-2013-2962"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Han","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025621521","display_name":"Yoshiharu Kohayakawa","orcid":"https://orcid.org/0000-0001-7841-157X"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Yoshiharu Kohayakawa","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077090568","display_name":"Yury Person","orcid":"https://orcid.org/0000-0002-3091-3025"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Yury Person","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Ilmenau, 98684 Ilmenau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Ilmenau, 98684 Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077090568"],"corresponding_institution_ids":["https://openalex.org/I119449181"],"apc_list":null,"apc_paid":null,"fwci":1.0939,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76262315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"30","issue":"4","first_page":"570","last_page":"590"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9991000294685364,"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":0.832230269908905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6410386562347412},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6208970546722412},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6076326966285706},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5873427391052246},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5645577907562256},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5534562468528748},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5383623242378235},{"id":"https://openalex.org/keywords/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.5275238156318665},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.46237704157829285},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4605611264705658},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4109051823616028},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.147751122713089},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13689839839935303},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09749272465705872}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.832230269908905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6410386562347412},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6208970546722412},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6076326966285706},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5873427391052246},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5645577907562256},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5534562468528748},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5383623242378235},{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.5275238156318665},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.46237704157829285},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4605611264705658},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4109051823616028},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.147751122713089},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13689839839935303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09749272465705872},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548320000577","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548320000577","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:003020458","is_oa":true,"landing_page_url":"https://doi.org/10.1017/S0963548320000577","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:003020458","is_oa":true,"landing_page_url":"https://doi.org/10.1017/S0963548320000577","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W287611495","https://openalex.org/W1623354552","https://openalex.org/W1639593279","https://openalex.org/W1998400388","https://openalex.org/W2004308928","https://openalex.org/W2005616548","https://openalex.org/W2011869755","https://openalex.org/W2054249991","https://openalex.org/W2055787252","https://openalex.org/W2059967030","https://openalex.org/W2068871408","https://openalex.org/W2069486179","https://openalex.org/W2088622619","https://openalex.org/W2110787567","https://openalex.org/W2113407082","https://openalex.org/W2127902766","https://openalex.org/W2159703794","https://openalex.org/W2478722229","https://openalex.org/W2560350525","https://openalex.org/W2601334854","https://openalex.org/W2803584453","https://openalex.org/W2964142729","https://openalex.org/W2964857609","https://openalex.org/W2999306665","https://openalex.org/W3104234497","https://openalex.org/W3144881883","https://openalex.org/W4237496336","https://openalex.org/W4239754724","https://openalex.org/W4249923855"],"related_works":["https://openalex.org/W2988803943","https://openalex.org/W3195404686","https://openalex.org/W1971174658","https://openalex.org/W3197756843","https://openalex.org/W2998159925","https://openalex.org/W2099195351","https://openalex.org/W2161451071","https://openalex.org/W2790612152","https://openalex.org/W2499670206","https://openalex.org/W2946244341"],"abstract_inverted_index":{"Abstract":[0],"We":[1,124],"prove":[2],"that,":[3],"for":[4,66,95],"any":[5,24],"$t":[6],"\\ge":[7],"3$":[8],",":[9,83,85],"there":[10],"exists":[11],"a":[12,96,120],"constant":[13,100],"c":[14,16,101],"=":[15],"(":[17,74,81],"t":[18,52],")":[19],">":[20,102],"0":[21,103],"such":[22],"that":[23,80],"d":[25,84],"-regular":[26],"n":[27,82,88],"-vertex":[28],"graph":[29],"with":[30,87,113],"the":[31,67,135],"second":[32],"largest":[33],"eigenvalue":[34],"in":[35,119,134],"absolute":[36,99],"value":[37],"\u03bb":[38],"satisfying":[39],"$\\lambda":[40,92],"\\le":[41,93],"c{d^{t":[42],"-":[43,45,59],"1}}/{n^{t":[44],"2}}$":[46],"contains":[47],"vertex-disjoint":[48],"copies":[49],"of":[50,69],"k":[51],"covering":[53],"all":[54],"but":[55],"at":[56],"most":[57],"${n^{1":[58],"1/(8{t^4})}}$":[60],"vertices.":[61],"This":[62],"provides":[63],"further":[64],"support":[65],"conjecture":[68],"Krivelevich,":[70],"Sudakov":[71],"and":[72,91,116],"Sz\u00e1bo":[73],"Combinatorica":[75],"24":[76],"(2004),":[77],"pp.":[78],"403\u2013426)":[79],"\u03bb)-graphs":[86],"\u2208":[89],"3\u2115":[90],"c{d^2}/n$":[94],"suitably":[97],"small":[98],"contain":[104],"triangle-factors.":[105],"Our":[106],"arguments":[107],"combine":[108],"tools":[109],"from":[110],"linear":[111],"programming":[112],"probabilistic":[114],"techniques,":[115],"apply":[117],"them":[118],"certain":[121],"weighted":[122],"setting.":[123],"expect":[125],"this":[126],"method":[127],"will":[128],"be":[129],"applicable":[130],"to":[131],"other":[132],"problems":[133],"field.":[136]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}