{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:12:16Z","timestamp":1761808336094,"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 the random hypergraph $H=H_{n,p;3}$ each possible triple appears independently with probability $p$. A loose Hamilton cycle can be described as a sequence of edges $\\{x_i,y_i,x_{i+1}\\}$ for $i=1,2,\\ldots,n\/2$ where $x_1,x_2,\\ldots,x_{n\/2},y_1,y_2,\\ldots,y_{n\/2}$ are all distinct. We prove that there exists an absolute constant $K&gt;0$ such that if $p\\geq {K\\log n\\over n^2}$ then  $$\\lim_{\\textstyle{n\\to \\infty\\atop 4|n}}\\Pr(H_{n,p;3}\\  contains\\ a\\ loose\\ Hamilton\\ cycle)=1.$$<\/jats:p>","DOI":"10.37236\/477","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:12:56Z","timestamp":1578715976000},"source":"Crossref","is-referenced-by-count":23,"title":["Loose Hamilton Cycles in Random 3-Uniform Hypergraphs"],"prefix":"10.37236","volume":"17","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,5,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:51:13Z","timestamp":1579305073000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1n28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,5,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/477","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,5,25]]},"article-number":"N28"}}