{"id":"https://openalex.org/W2104183200","doi":"https://doi.org/10.1017/s0963548300001796","title":"Perfect Matchings in Random <i>r</i>-regular, <i>s</i>-uniform Hypergraphs","display_name":"Perfect Matchings in Random <i>r</i>-regular, <i>s</i>-uniform Hypergraphs","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2104183200","doi":"https://doi.org/10.1017/s0963548300001796","mag":"2104183200"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548300001796","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300001796","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://utoronto.scholaris.ca/bitstreams/70298ce7-25c8-4898-8fef-0824519e5bc8/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":"Colin Cooper","raw_affiliation_strings":["School of Mathematical Sciences, University of North London, London, UK","* School of Mathematical Sciences, University of North London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of North London, London, UK","institution_ids":["https://openalex.org/I126193024"]},{"raw_affiliation_string":"* School of Mathematical Sciences, University of North London, London, UK","institution_ids":["https://openalex.org/I126193024"]}]},{"author_position":"middle","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":"Alan Frieze","raw_affiliation_strings":["Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pa. 15213 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pa. 15213 USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072889645","display_name":"Michael Molloy","orcid":"https://orcid.org/0000-0001-5435-1015"},"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":"Michael Molloy","raw_affiliation_strings":["Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pa. 15213 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pa. 15213 USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108103165","display_name":"Bruce Reed","orcid":"https://orcid.org/0009-0002-5656-8941"},"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":"Bruce Reed","raw_affiliation_strings":["Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pa. 15213 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Mathematics, Carnegie-Mellon University, Pittsburgh, Pa. 15213 USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4014,"has_fulltext":true,"cited_by_count":53,"citation_normalized_percentile":{"value":0.79596587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"1","last_page":"14"},"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":0.9994000196456909,"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":0.9994000196456909,"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/T11476","display_name":"Graph theory and applications","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9904999732971191,"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/hypergraph","display_name":"Hypergraph","score":0.8719819784164429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8238118886947632},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7526288032531738},{"id":"https://openalex.org/keywords/perfect-power","display_name":"Perfect power","score":0.672646164894104},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5685851573944092},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.48265963792800903},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44500258564949036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10480943322181702},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08945146203041077}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8719819784164429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8238118886947632},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7526288032531738},{"id":"https://openalex.org/C93446932","wikidata":"https://www.wikidata.org/wiki/Q1972803","display_name":"Perfect power","level":2,"score":0.672646164894104},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5685851573944092},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48265963792800903},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44500258564949036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10480943322181702},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08945146203041077},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1017/s0963548300001796","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300001796","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:utoronto.scholaris.ca:1807/9486","is_oa":true,"landing_page_url":"http://hdl.handle.net/1807/9486","pdf_url":"https://utoronto.scholaris.ca/bitstreams/70298ce7-25c8-4898-8fef-0824519e5bc8/download","source":{"id":"https://openalex.org/S7407055458","display_name":"TSpace","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},{"id":"pmh:oai:repository.cmu.edu:math-1511","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1511&context=math","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Mathematical Sciences","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6479114","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal contribution"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.113.4391","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.4391","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cgm.cs.mcgill.ca/~reedbook/papers/1996_COO_FR_MO_R.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.22.6146","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.6146","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~molloy/webpapers/hyper.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.1041","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.1041","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/~af1p/triples.ps.gz","raw_type":"text"},{"id":"doi:10.1184/r1/6479114","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6479114","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:utoronto.scholaris.ca:1807/9486","is_oa":true,"landing_page_url":"http://hdl.handle.net/1807/9486","pdf_url":"https://utoronto.scholaris.ca/bitstreams/70298ce7-25c8-4898-8fef-0824519e5bc8/download","source":{"id":"https://openalex.org/S7407055458","display_name":"TSpace","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.49000000953674316}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310207","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2104183200.pdf","grobid_xml":"https://content.openalex.org/works/W2104183200.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1963909248","https://openalex.org/W1997698259","https://openalex.org/W2007612705","https://openalex.org/W2013430224","https://openalex.org/W2068871408","https://openalex.org/W2072508453","https://openalex.org/W2091476183","https://openalex.org/W2100057426","https://openalex.org/W2111559003","https://openalex.org/W2136219960"],"related_works":["https://openalex.org/W3216169553","https://openalex.org/W3107721479","https://openalex.org/W3019763240","https://openalex.org/W3166438828","https://openalex.org/W2085440561","https://openalex.org/W1978240867","https://openalex.org/W2132073309","https://openalex.org/W3209968583","https://openalex.org/W2092296749","https://openalex.org/W132200507"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"r":[3],"-regular,":[4],"s":[5],"-uniform":[6],"hypergraphs":[7,36],"contain":[8],"a":[9,25],"perfect":[10,58,72],"matching":[11],"with":[12],"high":[13],"probability":[14],"(whp),":[15,85],"provided":[16],"The":[17,33,51],"Proof":[18],"is":[19,37,80],"based":[20],"on":[21],"the":[22,43,49,54,66,69,75,87],"application":[23],"of":[24,27,35,45,57,65,68,71,77],"technique":[26],"Robinson":[28],"and":[29,79],"Wormald":[30],"[7,":[31],"8].":[32],"space":[34,76],"partitioned":[38],"into":[39],"subsets":[40,62],"according":[41],"to":[42,82],"number":[44,56,70],"small":[46],"cycles":[47],"in":[48,53,74],"hypergraph.":[50],"difference":[52],"expected":[55],"matchings":[59,73],"between":[60],"these":[61],"explains":[63],"most":[64],"variance":[67],"hypergraphs,":[78],"sufficient":[81],"prove":[83],"existence":[84],"using":[86],"Chebychev":[88],"Inequality.":[89]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
