{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810294,"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>Given two $r$-uniform hypergraphs $F$ and $H$, we say that $H$ has an $F$-covering if every vertex in $H$ is contained in a copy of $F$. Let $c_{i}(n,F)$ be the least integer such that every $n$-vertex $r$-graph $H$ with $\\delta_{i}(H)&gt;c_i(n,F)$ has an $F$-covering. Falgas-Ravry, Markstr\u00f6m and Zhao (Combin. Probab. Comput., 2021) asymptotically determined $c_1(n,K_{4}^{(3)-})$, where $K_{4}^{(3)-}$ is obtained by deleting an edge from the complete $3$-graph on $4$ vertices. Later, Tang, Ma and Hou (Electron. J. Combin., 2023) asymptotically determined $c_1(n,C_{6}^{(3)})$, where $C_{6}^{(3)}$ is the linear triangle, i.e. $C_{6}^{(3)}=([6],\\{123,345,561\\})$. In this paper, we determine $c_1(n,F_5)$ asymptotically, where $F_5$ is the generalized triangle, i.e. $F_5=([5],\\{123,124,345\\})$. We also determine the exact values of $c_1(n,F)$, where $F$ is any connected $3$-graph with $3$ edges and $F\\notin\\{K_4^{(3)-}, C_{6}^{(3)}, F_5\\}$.<\/jats:p>","DOI":"10.37236\/12325","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T11:22:51Z","timestamp":1740655371000},"source":"Crossref","is-referenced-by-count":0,"title":["The Degree Threshold for Covering with all the Connected $3$-Graphs with $3$ Edges"],"prefix":"10.37236","volume":"32","author":[{"given":"Yue","family":"Ma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinmin","family":"Hou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Yin","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\/v32i1p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T11:22:51Z","timestamp":1740655371000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i1p34"}},"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\/12325","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,2,28]]},"article-number":"P1.34"}}