{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,4]],"date-time":"2023-11-04T00:49:37Z","timestamp":1699058977616},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"Given two $k$-uniform hypergraphs $F$ and $G$, we say that $G$ has an $F$-covering if every vertex in $G$ is contained in a copy of $F$. For $1\\le i \\le k-1$, let $c_i(n,F)$ be the least integer such that every $n$-vertex $k$-uniform hypergraph $G$ with $\\delta_i(G)> c_i(n,F)$ has an $F$-covering. The covering problem has been systematically studied by Falgas-Ravry and Zhao [Codegree thresholds for covering 3-uniform hypergraphs, [SIAM J. Discrete Math., 2016]. Last year, Falgas-Ravry, Markstr\u00f6m, and Zhao [Triangle-degrees in graphs and tetrahedron coverings in 3-graphs, Combinatorics, Probability and Computing, 2021] asymptotically determined $c_1(n, F)$ when $F$ is the generalized triangle. In this note, we give the exact value of $c_2(n, F)$ and asymptotically determine $c_1(n, F)$ when $F$ is the linear triangle $C_6^3$, where $C_6^3$ is the 3-uniform hypergraph with vertex set $\\{v_1,v_2,v_3,v_4,v_5,v_6\\}$ and edge set $\\{v_1v_2v_3,v_3v_4v_5,v_5v_6v_1\\}$.<\/jats:p>","DOI":"10.37236\/11717","type":"journal-article","created":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T14:14:52Z","timestamp":1699020892000},"source":"Crossref","is-referenced-by-count":0,"title":["The Degree and Codegree Threshold for Linear Triangle Covering in 3-Graphs"],"prefix":"10.37236","volume":"30","author":[{"given":"Yuxuan","family":"Tang","sequence":"first","affiliation":[]},{"given":"Yue","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Xinmin","family":"Hou","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,11,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T14:14:53Z","timestamp":1699020893000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i4p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,3]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,10,6]]}},"URL":"http:\/\/dx.doi.org\/10.37236\/11717","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,3]]}}}
