{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:26Z","timestamp":1753893806226,"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>We show that for $ \\eta&gt;0 $ and sufficiently large $ n $, every 5-graph on $ n $ vertices with $\\delta_{2}(H)\\ge (91\/216+\\eta)\\binom{n}{3}$ contains a Hamilton 2-cycle. This minimum 2-degree condition is asymptotically best possible. Moreover, we give some related results on minimum $ d $-degree conditions in $ k $-graphs that guarantee the existence of a Hamilton $ \\ell $-cycle when $\\ell\\le d \\le k-1$ and $1\\le \\ell &lt; k\/2$.<\/jats:p>","DOI":"10.37236\/12143","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T11:22:56Z","timestamp":1740655376000},"source":"Crossref","is-referenced-by-count":0,"title":["Minimum Degree Conditions for Hamilton $l$-Cycles in $k$-Uniform Hypergraphs"],"prefix":"10.37236","volume":"32","author":[{"given":"Jie","family":"Han","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghui","family":"Wang","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\/v32i1p35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T11:22:56Z","timestamp":1740655376000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i1p35"}},"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\/12143","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,2,28]]},"article-number":"P1.35"}}