{"id":"https://openalex.org/W2148175478","doi":"https://doi.org/10.1017/s0963548314000182","title":"Counting Independent Sets in Hypergraphs","display_name":"Counting Independent Sets in Hypergraphs","publication_year":2014,"publication_date":"2014-04-08","ids":{"openalex":"https://openalex.org/W2148175478","doi":"https://doi.org/10.1017/s0963548314000182","mag":"2148175478"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548314000182","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000182","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1310.6672","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"JEFF COOPER","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JEFF COOPER","raw_affiliation_strings":["Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, IL 60607, USA (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, IL 60607, USA (e-mail:","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"middle","author":{"id":null,"display_name":"KUNAL DUTTA","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"KUNAL DUTTA","raw_affiliation_strings":["Algorithms and Complexity Department, Max Planck Institute for Informatics, Saarbr\u00fccken, Germany (e-mail:"],"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity Department, Max Planck Institute for Informatics, Saarbr\u00fccken, Germany (e-mail:","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":null,"display_name":"DHRUV MUBAYI","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DHRUV MUBAYI","raw_affiliation_strings":["Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, IL 60607, USA (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, IL 60607, USA (e-mail:","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":1.111,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.75489068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"4","first_page":"539","last_page":"550"},"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":0.7876999974250793,"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":0.7876999974250793,"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":0.1664000004529953,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.015300000086426735,"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/hypergraph","display_name":"Hypergraph","score":0.8471999764442444},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.66839998960495},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.5723000168800354},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5705999732017517},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5564000010490417},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4675000011920929},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4072999954223633},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3346000015735626}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8471999764442444},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8388000130653381},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8077999949455261},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.66839998960495},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.5723000168800354},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5705999732017517},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5564000010490417},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4771000146865845},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4675000011920929},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.2973000109195709},{"id":"https://openalex.org/C53052385","wikidata":"https://www.wikidata.org/wiki/Q17104046","display_name":"Mixed graph","level":5,"score":0.2930999994277954},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.2768000066280365},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2612999975681305},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548314000182","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000182","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:1310.6672","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.6672","pdf_url":"https://arxiv.org/pdf/1310.6672","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1310.6672","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.6672","pdf_url":"https://arxiv.org/pdf/1310.6672","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1588434395","https://openalex.org/W1964543450","https://openalex.org/W1971289435","https://openalex.org/W1973915392","https://openalex.org/W2052723037","https://openalex.org/W2062230178","https://openalex.org/W2071474047","https://openalex.org/W2077204415","https://openalex.org/W2090984774","https://openalex.org/W2100437838","https://openalex.org/W2124088817","https://openalex.org/W2132680686","https://openalex.org/W2162218992","https://openalex.org/W3101393766","https://openalex.org/W4210634265"],"related_works":[],"abstract_inverted_index":{"Let":[0,111],"G":[1,17],"be":[2,113],"a":[3,29,82,107,114,134,163,190],"triangle-free":[4,49,83],"graph":[5,50,84],"with":[6,85,120],"n":[7,45,52,78,86,121],"vertices":[8,53,87,122],"and":[9,35,123,161,168],"average":[10,124],"degree":[11,125],"t":[12,126],".":[13,71,104,127],"We":[14,128],"show":[15,74,130],"that":[16,43,75,131,139],"contains":[18],"at":[19,55,90,148],"least":[20,56,149],"${\\exp\\biggl({1-n^{-1/12})\\frac{1}{2}\\frac{n}{t}\\ln":[21],"t}":[22],"\\biggl(\\frac{1}{2}\\ln":[23],"t-1\\biggr)\\biggr)}$":[24],"independent":[25,61,94,143,177],"sets.":[26],"This":[27,105,152],"improves":[28],"recent":[30],"result":[31,164],"of":[32,142,165,175,179,184,199],"the":[33,140,157,173],"first":[34],"third":[36],"authors":[37],"[8].":[38,110],"In":[39],"particular,":[40],"it":[41],"implies":[42],"as":[44],"\u2192":[46],"\u221e,":[47],"every":[48],"on":[51],"has":[54,89],"${e^{(c_1-o(1))":[57],"\\sqrt{n}":[58],"\\ln":[59],"n}}$":[60,93],"sets,":[62,95],"where":[63,96],"$c_1":[64],"=":[65,68,98,101],"\\sqrt{\\ln":[66],"2}/4":[67],"0.208138":[69],"\\ldots$":[70,103],"Further,":[72],"we":[73],"for":[76],"all":[77],",":[79],"there":[80,132],"exists":[81,133],"which":[88,171,194],"most":[91],"${e^{(c_2+o(1))\\sqrt{n}\\ln":[92],"$c_2":[97],"2\\sqrt{\\ln":[99],"2}":[100],"1.665109":[102],"disproves":[106],"conjecture":[108],"from":[109,156,189],"H":[112,146],"(":[115],"k":[116,137,160],"+1)-uniform":[117],"linear":[118],"hypergraph":[119],"also":[129],"constant":[135,158],"c":[136,159],"such":[138],"number":[141],"sets":[144],"in":[145],"is":[147,153],"${\\exp\\biggl({c_{k}":[150],"\\frac{n}{t^{1/k}}\\ln^{1+1/k}{t}\\biggr})}.$":[151],"tight":[154],"apart":[155],"generalizes":[162],"Duke,":[166],"Lefmann":[167],"R\u00f6dl":[169],"[9],":[170],"guarantees":[172],"existence":[174],"an":[176],"set":[178],"size":[180],"$\\Omega\\biggl(\\frac{n}{t^{1/k}}":[181],"\\ln^{1/k}t\\biggr).$":[182],"Both":[183],"our":[185],"lower":[186],"bounds":[187],"follow":[188],"more":[191],"general":[192],"statement,":[193],"applies":[195],"to":[196],"hereditary":[197],"properties":[198],"hypergraphs.":[200]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-28T06:11:35.319607","created_date":"2016-06-24T00:00:00"}