{"id":"https://openalex.org/W4248246025","doi":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<42::aid-jgt5>3.0.co;2-h","title":"Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at leastk","display_name":"Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at leastk","publication_year":2000,"publication_date":"2000-05-01","ids":{"openalex":"https://openalex.org/W4248246025","doi":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<42::aid-jgt5>3.0.co;2-h"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(200005)34:1<42::aid-jgt5>3.0.co;2-h","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<42::aid-jgt5>3.0.co;2-h","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5111515932","display_name":"B. Bollob\ufffds","orcid":null},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"B. Bollob\ufffds","raw_affiliation_strings":["Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152","institution_ids":["https://openalex.org/I94658018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022238950","display_name":"Colin Cooper","orcid":"https://orcid.org/0000-0002-5264-4401"},"institutions":[{"id":"https://openalex.org/I126193024","display_name":"London Metropolitan University","ror":"https://ror.org/00ae33288","country_code":"GB","type":"education","lineage":["https://openalex.org/I126193024"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"C. Cooper","raw_affiliation_strings":["School of Mathematical Sciences, University of North London, London N7 8DB, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of North London, London N7 8DB, UK","institution_ids":["https://openalex.org/I126193024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014473920","display_name":"Trevor Fenner","orcid":"https://orcid.org/0000-0002-4239-7574"},"institutions":[{"id":"https://openalex.org/I98259816","display_name":"Birkbeck, University of London","ror":"https://ror.org/02mb95055","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I98259816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"T. I. Fenner","raw_affiliation_strings":["Department of Computer Science, Birkbeck College, University of London, Malet Street, London, WC1 UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Birkbeck College, University of London, Malet Street, London, WC1 UK","institution_ids":["https://openalex.org/I98259816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. M. Frieze","raw_affiliation_strings":["Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111515932"],"corresponding_institution_ids":["https://openalex.org/I94658018"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.42534837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"34","issue":"1","first_page":"42","last_page":"59"},"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":1.0,"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":1.0,"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":0.9994999766349792,"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/T10849","display_name":"Finite Group Theory Research","score":0.9993000030517578,"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":0.9041367173194885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8551787734031677},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6833068132400513},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.596594512462616},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4727811813354492},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46554386615753174},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4374491572380066},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4316740334033966},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.426597535610199},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.42290306091308594},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06679117679595947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05412283539772034}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9041367173194885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8551787734031677},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6833068132400513},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.596594512462616},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4727811813354492},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46554386615753174},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4374491572380066},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4316740334033966},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.426597535610199},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.42290306091308594},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06679117679595947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05412283539772034},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(200005)34:1<42::aid-jgt5>3.0.co;2-h","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<42::aid-jgt5>3.0.co;2-h","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1552433097","https://openalex.org/W1963913579","https://openalex.org/W2009232680","https://openalex.org/W2011177468","https://openalex.org/W2013832448","https://openalex.org/W2043506669","https://openalex.org/W2071896207","https://openalex.org/W2136219960","https://openalex.org/W2169071224"],"related_works":["https://openalex.org/W4256429076","https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W2012063272","https://openalex.org/W2348092930","https://openalex.org/W3161230432","https://openalex.org/W2138685729","https://openalex.org/W2062850566","https://openalex.org/W4308716484","https://openalex.org/W1968154277"],"abstract_inverted_index":{"Let":[0,24],"Gn,m,k":[1,74],"denote":[2],"the":[3],"space":[4],"of":[5,49],"simple":[6],"graphs":[7],"with":[8,75],"n":[9,81],"vertices,":[10],"m":[11],"edges,":[12],"and":[13],"minimum":[14],"degree":[15],"at":[16],"least":[17],"k,":[18],"each":[19],"graph":[20],"G":[21,25,30],"being":[22],"equiprobable.":[23],"have":[26],"property":[27],"Ak,":[28],"if":[29,40,66],"contains":[31],"\u230a(k":[32],"\u2212":[33],"1)/2\u230b":[34],"edge":[35,46],"disjoint":[36,47],"Hamilton":[37],"cycles,":[38],"and,":[39],"k":[41,56],"is":[42,60],"even,":[43],"a":[44,61],"further":[45],"matching":[48],"size":[50],"\u230an/2\u230b.":[51],"We":[52],"prove":[53],"that,":[54],"for":[55],"\u2265":[57,68],"3,":[58],"there":[59],"constant":[62],"Ck":[63],"such":[64],"that":[65],"2m":[67],"Ckn":[69],"then":[70],"Ak":[71],"occurs":[72],"in":[73],"probability":[76],"tending":[77],"to":[78],"1":[79],"as":[80],"\u2192":[82],"\u221e.":[83],"\u00a9":[84],"2000":[85,96],"John":[86],"Wiley":[87],"&":[88],"Sons,":[89],"Inc.":[90],"J.":[91],"Graph":[92],"Theory":[93],"34:":[94],"42\u201359,":[95]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
