{"id":"https://openalex.org/W2167942150","doi":"https://doi.org/10.1017/s0963548300000559","title":"Threshold Functions for <i>H</i>-factors","display_name":"Threshold Functions for <i>H</i>-factors","publication_year":1993,"publication_date":"1993-06-01","ids":{"openalex":"https://openalex.org/W2167942150","doi":"https://doi.org/10.1017/s0963548300000559","mag":"2167942150"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548300000559","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300000559","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/A5083469386","display_name":"Noga Alon","orcid":"https://orcid.org/0000-0003-1332-4883"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Noga Alon","raw_affiliation_strings":["Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Raphael Yuster","raw_affiliation_strings":["Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083469386"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.26168224,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2","issue":"2","first_page":"137","last_page":"144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9984999895095825,"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":0.9980999827384949,"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":0.8948734998703003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.669660210609436},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5824993848800659},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5550409555435181},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.43332940340042114},{"id":"https://openalex.org/keywords/arboricity","display_name":"Arboricity","score":0.42612987756729126},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.42036837339401245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.350217342376709},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.1841072142124176},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.10988268256187439},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.051310449838638306}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8948734998703003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.669660210609436},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5824993848800659},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5550409555435181},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.43332940340042114},{"id":"https://openalex.org/C83204008","wikidata":"https://www.wikidata.org/wiki/Q4784907","display_name":"Arboricity","level":4,"score":0.42612987756729126},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.42036837339401245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.350217342376709},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.1841072142124176},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.10988268256187439},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.051310449838638306}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548300000559","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300000559","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1964089073","https://openalex.org/W1981234161","https://openalex.org/W2001021855","https://openalex.org/W2004578660","https://openalex.org/W2009232680","https://openalex.org/W2010042187","https://openalex.org/W2026143151","https://openalex.org/W2051240017","https://openalex.org/W2061496873","https://openalex.org/W2068871408","https://openalex.org/W2100061495","https://openalex.org/W2111559003","https://openalex.org/W2166965860","https://openalex.org/W2610479830","https://openalex.org/W2610729871","https://openalex.org/W2905110430","https://openalex.org/W6645489038"],"related_works":["https://openalex.org/W2358241443","https://openalex.org/W4282016561","https://openalex.org/W3092119098","https://openalex.org/W4255444748","https://openalex.org/W1987743836","https://openalex.org/W2053279533","https://openalex.org/W2915580243","https://openalex.org/W1910769293","https://openalex.org/W2368524975","https://openalex.org/W4362737182"],"abstract_inverted_index":{"Let":[0,62],"H":[1,33,39,55,64,74,82,87,94,115,139,154,167,180],"be":[2,10],"a":[3,11,21,71,85,92,97,137,165,193],"graph":[4,12,107],"on":[5,13],"h":[6,183],"vertices,":[7],"and":[8,125],"G":[9,19,25,108,143,171],"n":[14,90,132,148,160,176,185],"vertices.":[15],"An":[16],"H-factor":[17],"of":[18,24,27,32,38,54,70,73,190,195],"is":[20,40,45,77,96],"spanning":[22],"subgraph":[23],"consisting":[26],"n/h":[28],"vertex":[29,72],"disjoint":[30],"copies":[31],".":[34,75],"The":[35],"fractional":[36],"arboricity":[37],",":[41],"where":[42],"the":[43,67,102,105],"maximum":[44],"taken":[46],"over":[47],"all":[48],"subgraphs":[49],"(":[50,86,93,109,131,138,144,147,159,166,172,175],"V":[51],"\u2032,":[52],"E\u2032)":[53],"with":[56],"|":[57,59],"V\u2032":[58],"&gt;":[60],"1.":[61],"\u03b4(":[63,81],")":[65,83,95,112,133,140,161],"denote":[66],"minimum":[68],"degree":[69],"It":[76],"shown":[78],"that":[79,104,128],"if":[80],"&lt;":[84],"),":[88,168],"then":[89],"\u22121/":[91,136,164],"sharp":[98],"threshold":[99],"function":[100],"for":[101,129,157],"property":[103],"random":[106],"n,":[110,145,173],"p":[111,130,146,158,174],"contains":[113,178],"an":[114,153,179],"-factor.":[116],"That":[117],"is,":[118],"there":[119],"are":[120],"two":[121],"positive":[122],"constants":[123],"c":[124],"C":[126],"so":[127],"=":[134,162],"cn":[135],"almost":[141,169],"surely":[142,170],"))":[149,177],"does":[150],"not":[151],"have":[152],"-factor,":[155],"whereas":[156],"Cn":[163],"-factor":[181],"(provided":[182],"divides":[184],").":[186],"A":[187],"special":[188],"case":[189],"this":[191],"answers":[192],"problem":[194],"Erd\u0151s.":[196]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}