{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:12:18Z","timestamp":1761808338424,"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>In the random $k$-uniform hypergraph $H^{(k)}_{n,p}$ of order $n$, each possible $k$-tuple appears independently with probability $p$. A loose Hamilton cycle is a cycle of order $n$ in which\u00a0every pair of consecutive edges intersects in a single vertex. It was shown by Frieze that if $p\\geq c(\\log n)\/n^2$ for some absolute constant $c&gt;0$, then a.a.s. $H^{(3)}_{n,p}$ contains a loose Hamilton cycle, provided that $n$ is divisible by $4$. Subsequently, \u00a0Dudek and Frieze extended this result for any uniformity $k\\ge 4$, proving that if $p\\gg (\\log n)\/n^{k-1}$, then $H^{(k)}_{n,p}$ contains a loose Hamilton cycle, provided that $n$ is divisible by $2(k-1)$. In this paper, we improve the divisibility requirement and show that in the above results it is enough to assume that $n$ is a multiple of $k-1$, which is best possible.<\/jats:p>","DOI":"10.37236\/2523","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:09:58Z","timestamp":1578712198000},"source":"Crossref","is-referenced-by-count":15,"title":["Optimal Divisibility Conditions for Loose Hamilton Cycles in Random Hypergraphs"],"prefix":"10.37236","volume":"19","author":[{"given":"Andrzej","family":"Dudek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Po-Shen","family":"Loh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shelley","family":"Speiss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,12,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:22:09Z","timestamp":1579299729000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,13]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2523","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,12,13]]},"article-number":"P44"}}