{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T09:19:10Z","timestamp":1762161550925,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we study $r$-uniform hypergraphs ${\\cal H}$ without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for $r = 3$, we show that if ${\\cal H}$ has $n$ vertices and a maximum number of edges, then $$|{\\cal H}|={\\textstyle 1\\over6}n^{3\/2} + o(n^{3\/2}).$$ This also asymptotically determines  the generalized Tur\u00e1n number $T_{3}(n,8,4)$. Some results are based on our bounds for the maximum size of Sidon-type sets in $\\Bbb{Z}_{n}$.<\/jats:p>","DOI":"10.37236\/1718","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:28:53Z","timestamp":1578709733000},"source":"Crossref","is-referenced-by-count":43,"title":["On Hypergraphs of Girth Five"],"prefix":"10.37236","volume":"10","author":[{"given":"Felix","family":"Lazebnik","sequence":"first","affiliation":[]},{"given":"Jacques","family":"Verstra\u00ebte","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2003,5,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:07:41Z","timestamp":1579324061000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1718","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,5,30]]},"article-number":"R25"}}