{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:04Z","timestamp":1753893784460,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Denote by $F_5$ the $3$-uniform hypergraph on vertex set $\\{1,2,3,4,5\\}$ with hyperedges $\\{123,124,345\\}$. Balogh, Butterfield, Hu, and Lenz proved that if $p &gt; K \\log n \/n$ for some large constant $K$, then every maximum $F_5$-free subhypergraph of $G^3(n,p)$ is tripartite with high probability, and showed that if $p_0 = 0.1\\sqrt{\\log n} \/n$, then with high probability there exists a maximum $F_5$-free subhypergraph of $G^3(n,p_0)$ that is not tripartite. In this paper, we sharpen the upper bound to be best possible up to a constant factor. We prove that if $p &gt; C \\sqrt{\\log n} \/n $ for some large constant $C$, then every maximum $F_5$-free subhypergraph of $G^3(n, p)$ is tripartite with high probability.<\/jats:p>","DOI":"10.37236\/11328","type":"journal-article","created":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T14:14:54Z","timestamp":1699020894000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Maximum $F_5$-Free Subhypergraphs of a Random Hypergraph"],"prefix":"10.37236","volume":"30","author":[{"given":"Igor","family":"Araujo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00f3zsef","family":"Balogh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoran","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,11,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p22\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T14:14:55Z","timestamp":1699020895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i4p22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,3]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,10,6]]}},"URL":"https:\/\/doi.org\/10.37236\/11328","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,11,3]]},"article-number":"P4.22"}}