{"id":"https://openalex.org/W2150075045","doi":"https://doi.org/10.37236/1718","title":"On Hypergraphs of Girth Five","display_name":"On Hypergraphs of Girth Five","publication_year":2003,"publication_date":"2003-05-30","ids":{"openalex":"https://openalex.org/W2150075045","doi":"https://doi.org/10.37236/1718","mag":"2150075045"},"language":"en","primary_location":{"id":"doi:10.37236/1718","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1718","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r25/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":false,"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":null,"license_id":null,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r25/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031529103","display_name":"Felix Lazebnik","orcid":null},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Felix Lazebnik","raw_affiliation_strings":["Department of Mathematical Sciences University of Delaware, Newark, DE 19716, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences University of Delaware, Newark, DE 19716, USA","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024446850","display_name":"Jacques Verstra\u00ebte","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jacques Verstra\u00ebte","raw_affiliation_strings":["Theory Group, Microsoft Research Building 113/2105 Redmond, WA 98052, USA"],"affiliations":[{"raw_affiliation_string":"Theory Group, Microsoft Research Building 113/2105 Redmond, WA 98052, USA","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031529103"],"corresponding_institution_ids":["https://openalex.org/I86501945"],"apc_list":null,"apc_paid":null,"fwci":1.1027,"has_fulltext":true,"cited_by_count":76,"citation_normalized_percentile":{"value":0.75728643,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"10","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9896000027656555,"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/mathematics","display_name":"Mathematics","score":0.9351197481155396},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8970393538475037},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.8786917924880981},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.7603089809417725},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43220826983451843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33648455142974854}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9351197481155396},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8970393538475037},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8786917924880981},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.7603089809417725},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43220826983451843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33648455142974854},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.37236/1718","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1718","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r25/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.10.2412","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.2412","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_10/PDF/v10i1r25.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.821","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_10/PostScriptfiles/v10i1r25.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.407.5148","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.407.5148","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.udel.edu/~lazebnik/papers/girth5finalEJC.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.5709","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.5709","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/~jverstra/hypergirth.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.868.6332","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.868.6332","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mast.queensu.ca/%7Egregoryd/decaen/Dom/LazVer.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.870.2486","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.870.2486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Felix_Lazebnik/publication/2877999_On_Hypergraphs_of_Girth_Five/links/0c96051531bf13fd68000000.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1718","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1718","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r25/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2150075045.pdf","grobid_xml":"https://content.openalex.org/works/W2150075045.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W7523768","https://openalex.org/W111038805","https://openalex.org/W1268512041","https://openalex.org/W1444168583","https://openalex.org/W1496730621","https://openalex.org/W1510730180","https://openalex.org/W1519229378","https://openalex.org/W1556771345","https://openalex.org/W1966969478","https://openalex.org/W2009852526","https://openalex.org/W2010961669","https://openalex.org/W2011729369","https://openalex.org/W2030243808","https://openalex.org/W2061342454","https://openalex.org/W2082547866","https://openalex.org/W2090534913","https://openalex.org/W2096590808","https://openalex.org/W2104498537","https://openalex.org/W2117908084","https://openalex.org/W2143569998","https://openalex.org/W2169722458","https://openalex.org/W2951084708","https://openalex.org/W4234803039","https://openalex.org/W4247203980","https://openalex.org/W6628667382","https://openalex.org/W6633621516"],"related_works":["https://openalex.org/W2963464045","https://openalex.org/W2150075045","https://openalex.org/W2755210407","https://openalex.org/W4236390637","https://openalex.org/W1978042415","https://openalex.org/W2085440561","https://openalex.org/W3047600982","https://openalex.org/W2132073309","https://openalex.org/W2964792792","https://openalex.org/W2092296749"],"abstract_inverted_index":{"In":[0,26],"this":[1],"paper,":[2],"we":[3,32],"study":[4],"$r$-uniform":[5],"hypergraphs":[6],"${\\cal":[7,36],"H}$":[8,37],"without":[9],"cycles":[10],"of":[11,19,45,73],"length":[12],"less":[13],"than":[14],"five,":[15],"employing":[16],"the":[17,57,70],"definition":[18],"a":[20,42],"hypergraph":[21],"cycle":[22],"due":[23],"to":[24],"Berge.":[25],"particular,":[27],"for":[28,69],"$r":[29],"=":[30],"3$,":[31],"show":[33],"that":[34],"if":[35],"has":[38],"$n$":[39],"vertices":[40],"and":[41],"maximum":[43,71],"number":[44,60],"edges,":[46],"then":[47],"$$|{\\cal":[48],"H}|={\\textstyle":[49],"1\\over6}n^{3/2}":[50],"+":[51],"o(n^{3/2}).$$":[52],"This":[53],"also":[54],"asymptotically":[55],"determines":[56],"generalized":[58],"Tur\u00e1n":[59],"$T_{3}(n,8,4)$.":[61],"Some":[62],"results":[63],"are":[64],"based":[65],"on":[66],"our":[67],"bounds":[68],"size":[72],"Sidon-type":[74],"sets":[75],"in":[76],"$\\Bbb{Z}_{n}$.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}