{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:24:43Z","timestamp":1759335883047,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For $1\\leq \\ell&lt; k$,\u00a0 an\u00a0$\\ell$-overlapping $k$-cycle\u00a0is 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\u00a0if $H$ does not contain an $\\ell$-overlapping hamiltonian $k$-cycle but every hypergraph obtained from $H$ by adding one edge does contain such a cycle. Let sat$(N,k,\\ell)$ be the smallest number of edges in an $\\ell$-hamiltonian saturated $k$-uniform hypergraph on $N$ vertices. In the case of graphs Clark and Entringer showed in 1983 that sat$(N,2,1)=\\lceil \\tfrac{3N}2\\rceil$. The present authors proved that for $k\\geq 3$ and $\\ell=1$, as well as for all $0.8k\\leq \\ell\\leq k-1$, sat$(N,k,\\ell)=\\Theta(N^{\\ell})$. Here we prove that sat$(N,2\\ell,\\ell)=\\Theta\\left(N^\\ell\\right)$.<\/jats:p>","DOI":"10.37236\/8414","type":"journal-article","created":{"date-parts":[[2020,12,5]],"date-time":"2020-12-05T09:00:56Z","timestamp":1607158856000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Minimum Size of Hamilton Saturated Hypergraphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Andrzej","family":"Ruci\u0144ski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrzej","family":"\u017bak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,11,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,5]],"date-time":"2020-12-05T09:00:56Z","timestamp":1607158856000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,27]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/8414","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,11,27]]},"article-number":"P4.36"}}