{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:13:33Z","timestamp":1761808413430,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A Hamilton Berge cycle of a hypergraph on $n$ vertices is an alternating sequence $(v_1, e_1, v_2, \\ldots, v_n, e_n)$ of distinct vertices $v_1, \\ldots, v_n$ and distinct hyperedges $e_1, \\ldots, e_n$ such that $\\{v_1,v_n\\}\\subseteq e_n$ and $\\{v_i, v_{i+1}\\} \\subseteq e_i$ for every $i\\in [n-1]$. We prove the following Dirac-type theorem about Berge cycles in the binomial random $r$-uniform hypergraph $H^{(r)}(n,p)$: for every integer $r \\geq 3$, every real $\\gamma&gt;0$ and\u00a0$p \\geq \\frac{\\ln^{17r} n}{n^{r-1}}$ asymptotically almost surely,\u00a0 every spanning subgraph $H \\subseteq H^{(r)}(n,p)$ with\u00a0 minimum vertex degree $\\delta_1(H) \\geq \\left(\\frac{1}{2^{r-1}} + \\gamma\\right) p \\binom{n}{r-1}$ contains a Hamilton Berge cycle. The minimum degree condition is asymptotically tight and the bound on $p$ is optimal up to some polylogarithmic factor. \u00a0<\/jats:p>","DOI":"10.37236\/8611","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:50Z","timestamp":1599187670000},"source":"Crossref","is-referenced-by-count":6,"title":["A Dirac-type Theorem for Berge Cycles in Random Hypergraphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Dennis","family":"Clemens","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julia","family":"Ehrenm\u00fcller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yury","family":"Person","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,8,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p39\/8157","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p39\/8157","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:47:50Z","timestamp":1599187670000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,21]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8611","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,8,21]]},"article-number":"P3.39"}}