{"id":"https://openalex.org/W3094179932","doi":"https://doi.org/10.37236/9604","title":"The Maximum Number of Cliques in Hypergraphs without Large Matchings","display_name":"The Maximum Number of Cliques in Hypergraphs without Large Matchings","publication_year":2020,"publication_date":"2020-10-16","ids":{"openalex":"https://openalex.org/W3094179932","doi":"https://doi.org/10.37236/9604","mag":"3094179932"},"language":"en","primary_location":{"id":"doi:10.37236/9604","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9604","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p14/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p14/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088530178","display_name":"Erica L.L. Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Erica L.L. Liu","raw_affiliation_strings":["Center for Applied Mathematics. Tianjin University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics. Tianjin University","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101690212","display_name":"Jian Wang","orcid":"https://orcid.org/0000-0002-9134-1665"},"institutions":[{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Wang","raw_affiliation_strings":["Department of Mathematics, Taiyuan University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taiyuan University of Technology","institution_ids":["https://openalex.org/I9086337"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6427,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82282375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"27","issue":"4","first_page":null,"last_page":null},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9983999729156494,"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/T11476","display_name":"Graph theory and applications","score":0.994700014591217,"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":0.9511114358901978},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9166910648345947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8163716793060303},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6505396366119385},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6450580954551697},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6037082672119141},{"id":"https://openalex.org/keywords/rainbow","display_name":"Rainbow","score":0.47562626004219055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35991519689559937},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.19229155778884888},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07208257913589478}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.9511114358901978},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9166910648345947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8163716793060303},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6505396366119385},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6450580954551697},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6037082672119141},{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.47562626004219055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35991519689559937},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.19229155778884888},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07208257913589478},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9604","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9604","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p14/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/9604","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9604","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p14/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1713545879","display_name":null,"funder_award_id":"201801D221028","funder_id":"https://openalex.org/F4320326179","funder_display_name":"Shanxi Province Science Foundation for Youths"},{"id":"https://openalex.org/G2645222771","display_name":null,"funder_award_id":"11701407","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326179","display_name":"Shanxi Province Science Foundation for Youths","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3094179932.pdf","grobid_xml":"https://content.openalex.org/works/W3094179932.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1506116723","https://openalex.org/W2019935404","https://openalex.org/W2083155064","https://openalex.org/W2115164934","https://openalex.org/W2337826307","https://openalex.org/W2581786300","https://openalex.org/W2947735575","https://openalex.org/W2963861976","https://openalex.org/W4394670555","https://openalex.org/W6671561355"],"related_works":["https://openalex.org/W2394414377","https://openalex.org/W2386551956","https://openalex.org/W2374811656","https://openalex.org/W2500362344","https://openalex.org/W2759102619","https://openalex.org/W1480985150","https://openalex.org/W223516324","https://openalex.org/W2228017700","https://openalex.org/W2019539023","https://openalex.org/W4385757749"],"abstract_inverted_index":{"Let":[0],"$[n]$":[1,19,30],"denote":[2],"the":[3,16,26,47,58,73,83,107,118,138,158],"set":[4,18,22],"$\\{1,":[5],"2,":[6],"\\ldots,":[7],"n\\}$":[8],"and":[9,66,77,163],"$\\mathcal{F}^{(r)}_{n,k,a}$":[10,105],"be":[11],"an":[12],"$r$-uniform":[13,52,112,145],"hypergraph":[14,90,146],"on":[15,54,82,114,137],"vertex":[17],"with":[20,57,117],"edge":[21],"consisting":[23],"of":[24,29,49,72,85,96,109,140,152,160],"all":[25],"$r$-element":[27],"subsets":[28],"that":[31,44,104],"contains":[32],"at":[33,61,121],"least":[34],"$a$":[35],"vertices":[36,56,116],"in":[37,51,111],"$[ak+a-1]$.":[38],"For":[39],"$n\\geq":[40],"2rk$,":[41],"Frankl":[42],"proved":[43],"$\\mathcal{F}^{(r)}_{n,k,1}$":[45],"maximizes":[46,106],"number":[48,60,84,108,120,139],"edges":[50,86],"hypergraphs":[53,113],"$n$":[55,115],"matching":[59,75,95,119,151],"most":[62,122],"$k$.":[63,98],"Huang,":[64,161],"Loh":[65,162],"Sudakov":[67,164],"considered":[68],"a":[69,79,88,93,135,143,149],"multicolored":[70,89,144],"version":[71],"Erd\\H{o}s":[74],"conjecture,":[76],"provided":[78],"sufficient":[80],"condition":[81,136,159],"for":[87,124,142],"to":[91,147,157],"contain":[92,148],"rainbow":[94,150],"size":[97,153],"In":[99],"this":[100],"paper,":[101],"we":[102],"show":[103],"$s$-cliques":[110],"$k$":[123],"sufficiently":[125],"large":[126],"$n$,":[127],"where":[128],"$a=\\lfloor":[129],"\\frac{s-r}{k}":[130],"\\rfloor+1$.":[131],"We":[132],"also":[133],"obtain":[134],"$s$-clques":[141],"$k$,":[154],"which":[155],"reduces":[156],"when":[165],"$s=r$.":[166]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}