{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:24:22Z","timestamp":1759335862019,"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>For $1\\leq \\ell&lt; k$,\u00a0 an $\\ell$-overlapping cycle is a $k$-uniform hypergraph in which, for some cyclic vertex ordering, every edge consists of $k$ consecutive vertices and every two consecutive edges share exactly $\\ell$ vertices. A $k$-uniform hypergraph $H$ is $\\ell$-Hamiltonian saturated, $1\\le \\ell\\le k-1$, if $H$ does not contain an $\\ell$-overlapping Hamiltonian cycle $C^{(k)}_n(\\ell)$ but every hypergraph obtained from $H$ by adding one more edge does contain $C^{(k)}_n(\\ell)$. Let $sat(n,k,\\ell)$ be the smallest number of edges in an $\\ell$-Hamiltonian saturated $k$-uniform hypergraph on $n$ vertices. Clark and Entringer proved in 1983 that $sat(n,2,1)=\\lceil \\tfrac{3n}2\\rceil$ and the second author showed recently that $sat(n,k,k-1)=\\Theta(n^{k-1})$ for every $k\\ge2$. In this paper we prove that $sat(n,k,\\ell)=\\Theta(n^{\\ell})$ for $\\ell=1$ as well as for all $k\\ge5$ and $\\ell\\ge0.8k$.<\/jats:p>","DOI":"10.37236\/2484","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:46:55Z","timestamp":1578707215000},"source":"Crossref","is-referenced-by-count":1,"title":["Hamilton Saturated Hypergraphs of Essentially Minimum Size"],"prefix":"10.37236","volume":"20","author":[{"given":"Andrzej","family":"Ruci\u0144ski","sequence":"first","affiliation":[]},{"given":"Andrzej","family":"\u017bak","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,5,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:20:51Z","timestamp":1579260051000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,9]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/2484","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,5,9]]},"article-number":"P25"}}