{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:55:30Z","timestamp":1759118130501,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $H_{n,p,r}^{(k)}$ denote a randomly colored random hypergraph, constructed on the vertex set $[n]$ by taking each $k$-tuple independently with probability $p$, and then independently coloring it with a random color from the set $[r]$. Let $H$ be a $k$-uniform hypergraph of order $n$. An $\\ell$-Hamilton cycle\u00a0is a spanning subhypergraph $C$ of $H$ with $n\/(k-\\ell)$ edges and such that for some cyclic ordering of the vertices each edge of $C$ consists of $k$ consecutive vertices and every pair of adjacent edges in $C$ intersects in precisely $\\ell$ vertices.In this note we study the existence of rainbow $\\ell$-Hamilton cycles (that is every edge receives a different color) in $H_{n,p,r}^{(k)}$. We mainly focus on the most restrictive case when $r = n\/(k-\\ell)$. In particular, we show that for the so called tight Hamilton cycles ($\\ell=k-1$) $p = e^2\/n$ is the sharp threshold for the existence of a rainbow tight Hamilton cycle in $H_{n,p,n}^{(k)}$ for each $k\\ge 4$.<\/jats:p>","DOI":"10.37236\/7274","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:23:42Z","timestamp":1578669822000},"source":"Crossref","is-referenced-by-count":4,"title":["On Rainbow Hamilton Cycles in Random Hypergraphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Andrzej","family":"Dudek","sequence":"first","affiliation":[]},{"given":"Sean","family":"English","sequence":"additional","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,6,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p55\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p55\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:31:05Z","timestamp":1579235465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7274","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,6,22]]},"article-number":"P2.55"}}