{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813687,"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>Dirac proved that each $n$-vertex $2$-connected graph with minimum degree $k$ contains a cycle of length at least $\\min\\{2k, n\\}$. We obtain analogous results for Berge cycles in hypergraphs. Recently, the authors proved an exact lower bound on the minimum degree ensuring a Berge cycle of length at least $\\min\\{2k, n\\}$ in $n$-vertex $r$-uniform $2$-connected hypergraphs when $k \\geq r+2$. In this paper we address the case $k \\leq r+1$ in which the bounds have a different behavior. We prove that each $n$-vertex $r$-uniform $2$-connected hypergraph $H$ with minimum degree $k$ contains a Berge cycle of length at least $\\min\\{2k,n,|E(H)|\\}$. If $|E(H)|\\geq n$, this bound coincides with the bound of the Dirac's Theorem for 2-connected graphs.<\/jats:p>","DOI":"10.37236\/12486","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T11:22:43Z","timestamp":1740655363000},"source":"Crossref","is-referenced-by-count":0,"title":["A Hypergraph Analog  of Dirac's Theorem for Long Cycles in 2-Connected Graphs, II: Large Uniformities"],"prefix":"10.37236","volume":"32","author":[{"given":"Alexandr","family":"Kostochka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruth","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grace","family":"McCourt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,2,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T11:22:44Z","timestamp":1740655364000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i1p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1,17]]}},"URL":"https:\/\/doi.org\/10.37236\/12486","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,2,28]]},"article-number":"P1.31"}}