{"id":"https://openalex.org/W2032160258","doi":"https://doi.org/10.1017/s096354831200034x","title":"(<i>k</i>+1)-Cores Have <i>k</i>-Factors","display_name":"(<i>k</i>+1)-Cores Have <i>k</i>-Factors","publication_year":2012,"publication_date":"2012-09-11","ids":{"openalex":"https://openalex.org/W2032160258","doi":"https://doi.org/10.1017/s096354831200034x","mag":"2032160258"},"language":"en","primary_location":{"id":"doi:10.1017/s096354831200034x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831200034x","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/A5100856892","display_name":"Siu On Chan","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"SIU ON CHAN","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Ontario, Canada (e-mail:","Department of computer science, university of toronto, ontario, canada (e-mail: siuon@cs.toronto.edu, molloy@cs.toronto.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Ontario, Canada (e-mail:","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of computer science, university of toronto, ontario, canada (e-mail: siuon@cs.toronto.edu, molloy@cs.toronto.edu)#TAB#","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072889645","display_name":"Michael Molloy","orcid":"https://orcid.org/0000-0001-5435-1015"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"MICHAEL MOLLOY","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Ontario, Canada (e-mail:","Department of computer science, university of toronto, ontario, canada (e-mail: siuon@cs.toronto.edu, molloy@cs.toronto.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Ontario, Canada (e-mail:","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of computer science, university of toronto, ontario, canada (e-mail: siuon@cs.toronto.edu, molloy@cs.toronto.edu)#TAB#","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4202,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.87797282,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"6","first_page":"882","last_page":"896"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9991999864578247,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7423179149627686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6752085089683533},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5378242135047913},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.4259825050830841},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3391636312007904},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2308376431465149},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.0789901614189148}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7423179149627686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6752085089683533},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5378242135047913},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.4259825050830841},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3391636312007904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2308376431465149},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0789901614189148}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s096354831200034x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831200034x","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":10,"referenced_works":["https://openalex.org/W390146837","https://openalex.org/W1966530078","https://openalex.org/W1967786343","https://openalex.org/W2065663455","https://openalex.org/W2087348204","https://openalex.org/W2170981586","https://openalex.org/W3100131557","https://openalex.org/W3141776272","https://openalex.org/W4245919572","https://openalex.org/W4256646394"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"the":[3,6,21,24],"threshold":[4,22],"for":[5,23],"appearance":[7,25],"of":[8,26,36,46],"a":[9,27,34,44],"k":[10,30],"-regular":[11],"subgraph":[12],"in":[13],"G":[14],"n":[15],",":[16],"p":[17],"is":[18],"at":[19],"most":[20],"non-empty":[28],"(":[29],"+1)-core.":[31],"This":[32],"improves":[33],"result":[35],"Pralat,":[37],"Verstraete":[38,50],"and":[39,42,49],"Wormald":[40],"[5]":[41],"proves":[43],"conjecture":[45],"Bollob\u00e1s,":[47],"Kim":[48],"[3].":[51]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
