{"id":"https://openalex.org/W1538980689","doi":"https://doi.org/10.1017/s096354831800010x","title":"Largest Components in Random Hypergraphs","display_name":"Largest Components in Random Hypergraphs","publication_year":2018,"publication_date":"2018-04-04","ids":{"openalex":"https://openalex.org/W1538980689","doi":"https://doi.org/10.1017/s096354831800010x","mag":"1538980689"},"language":"en","primary_location":{"id":"doi:10.1017/s096354831800010x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831800010x","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1412.6366","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050468373","display_name":"Oliver Cooley","orcid":"https://orcid.org/0000-0002-9914-8210"},"institutions":[{"id":"https://openalex.org/I2799411422","display_name":"Center for Discrete Mathematics and Theoretical Computer Science","ror":"https://ror.org/00k551w06","country_code":"US","type":"facility","lineage":["https://openalex.org/I102322142","https://openalex.org/I118347220","https://openalex.org/I1283103587","https://openalex.org/I1311060795","https://openalex.org/I20089843","https://openalex.org/I2799411422","https://openalex.org/I4210107353"]},{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT","US"],"is_corresponding":true,"raw_author_name":"OLIVER COOLEY","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria (e-mail:","Institute of Discrete Mathematics (5050)"],"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria (e-mail:","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Institute of Discrete Mathematics (5050)","institution_ids":["https://openalex.org/I2799411422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002103922","display_name":"Mihyun Kang","orcid":"https://orcid.org/0000-0001-8729-2779"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]},{"id":"https://openalex.org/I2799411422","display_name":"Center for Discrete Mathematics and Theoretical Computer Science","ror":"https://ror.org/00k551w06","country_code":"US","type":"facility","lineage":["https://openalex.org/I102322142","https://openalex.org/I118347220","https://openalex.org/I1283103587","https://openalex.org/I1311060795","https://openalex.org/I20089843","https://openalex.org/I2799411422","https://openalex.org/I4210107353"]}],"countries":["AT","US"],"is_corresponding":false,"raw_author_name":"MIHYUN KANG","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria (e-mail:","Institute of Discrete Mathematics (5050)"],"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria (e-mail:","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Institute of Discrete Mathematics (5050)","institution_ids":["https://openalex.org/I2799411422"]}]},{"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/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BG","CZ","DE"],"is_corresponding":false,"raw_author_name":"YURY PERSON","raw_affiliation_strings":["Goethe-Universit\u00e4t, Institute of Mathematics, Robert-Mayer-Strasse 10, 60325 Frankfurt, Germany (e-mail:","Institute of Mathematics"],"affiliations":[{"raw_affiliation_string":"Goethe-Universit\u00e4t, Institute of Mathematics, Robert-Mayer-Strasse 10, 60325 Frankfurt, Germany (e-mail:","institution_ids":["https://openalex.org/I114090438"]},{"raw_affiliation_string":"Institute of Mathematics","institution_ids":["https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050468373"],"corresponding_institution_ids":["https://openalex.org/I2799411422","https://openalex.org/I4092182"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.003622,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"5","first_page":"741","last_page":"762"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.995199978351593,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.7512823343276978},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7487154603004456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7322514653205872},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.6661859750747681},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6000819206237793},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.5669777989387512},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.5638344287872314},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5321233868598938},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5219837427139282},{"id":"https://openalex.org/keywords/giant-component","display_name":"Giant component","score":0.5072557330131531},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4981820583343506},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4903114140033722},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4482937157154083},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4365957975387573},{"id":"https://openalex.org/keywords/transitive-closure","display_name":"Transitive closure","score":0.43336358666419983}],"concepts":[{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.7512823343276978},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7487154603004456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7322514653205872},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.6661859750747681},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6000819206237793},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.5669777989387512},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.5638344287872314},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5321233868598938},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5219837427139282},{"id":"https://openalex.org/C148818006","wikidata":"https://www.wikidata.org/wiki/Q4137985","display_name":"Giant component","level":4,"score":0.5072557330131531},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4981820583343506},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4903114140033722},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4482937157154083},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4365957975387573},{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.43336358666419983},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s096354831800010x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831800010x","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:arXiv.org:1412.6366","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.6366","pdf_url":"https://arxiv.org/pdf/1412.6366","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.1412.6366","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1412.6366","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},{"id":"mag:1538980689","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1412.6366","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.6366","pdf_url":"https://arxiv.org/pdf/1412.6366","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1538980689.pdf","grobid_xml":"https://content.openalex.org/works/W1538980689.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W390146837","https://openalex.org/W1889601917","https://openalex.org/W1977759320","https://openalex.org/W1982869544","https://openalex.org/W1983610133","https://openalex.org/W2018582120","https://openalex.org/W2040419749","https://openalex.org/W2043114757","https://openalex.org/W2047467760","https://openalex.org/W2073443682","https://openalex.org/W2079728415","https://openalex.org/W2080289118","https://openalex.org/W2093252122","https://openalex.org/W2106456894","https://openalex.org/W2110089205","https://openalex.org/W2160478770","https://openalex.org/W2161355281","https://openalex.org/W2478722229","https://openalex.org/W2949850753","https://openalex.org/W2952227056","https://openalex.org/W3144881883","https://openalex.org/W4241669766","https://openalex.org/W4243384247","https://openalex.org/W6639541036"],"related_works":["https://openalex.org/W2964352504","https://openalex.org/W2999148156","https://openalex.org/W2108540837","https://openalex.org/W2949085900","https://openalex.org/W2410349171","https://openalex.org/W3099640509","https://openalex.org/W3102138966","https://openalex.org/W3008018122","https://openalex.org/W2951496300","https://openalex.org/W3033267762","https://openalex.org/W2963327389","https://openalex.org/W2761339831","https://openalex.org/W2979697317","https://openalex.org/W2951946195","https://openalex.org/W3006967677","https://openalex.org/W1729121616","https://openalex.org/W2262634370","https://openalex.org/W3188814636","https://openalex.org/W2934612306","https://openalex.org/W3166040397"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"j":[5,14,23,41,58,64,66],"-tuple-connected":[6,59],"components":[7],"in":[8,30,130],"random":[9,110],"k":[10],"-uniform":[11],"hypergraphs":[12],"(the":[13],"-tuple-connectedness":[15],"relation":[16],"can":[17],"be":[18,25],"defined":[19],"by":[20,93],"letting":[21],"two":[22],"-sets":[24,67],"connected":[26],"if":[27],"they":[28],"lie":[29],"a":[31,57,69,101,109,117],"common":[32,47],"edge":[33,79],"and":[34,72,95],"considering":[35],"the":[36,39,46,54,75,85,90,106,124,127,131],"transitive":[37],"closure;":[38],"case":[40,92],"=":[42],"1":[43],"corresponds":[44],"to":[45,104],"notion":[48],"of":[49,56,100,108,126],"vertex-connectedness).":[50],"We":[51],"show":[52,73],"that":[53,74],"existence":[55],"component":[60,128],"containing":[61],"\u0398(":[62],"n":[63],")":[65],"undergoes":[68],"phase":[70],"transition":[71],"threshold":[76],"occurs":[77],"at":[78],"probability":[80],"$$\\frac{(k-j)!}{\\binom{k}{j}-1}n^{j-k}.$$":[81],"Our":[82,112],"proof":[83,88],"extends":[84],"recent":[86],"short":[87],"for":[89],"graph":[91],"Krivelevich":[94],"Sudakov,":[96],"which":[97,122],"makes":[98],"use":[99],"depth-first":[102],"search":[103,132],"reveal":[105],"edges":[107],"graph.":[111],"main":[113],"original":[114],"contribution":[115],"is":[116],"bounded":[118],"degree":[119],"lemma":[120],",":[121],"controls":[123],"structure":[125],"grown":[129],"process.":[133]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}