{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836567,"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>A classical result from graph theory is that every graph with chromatic number $\\chi &gt; t$ contains a subgraph with all degrees at least $t$, and therefore contains a copy of every $t$-edge tree. Bohman, Frieze, and Mubayi recently posed this problem for $r$-uniform hypergraphs.  An $r$-tree is a connected $r$-uniform hypergraph with no pair of edges intersecting in more than one vertex, and no sequence of distinct vertices and edges $(v_1, e_1, \\ldots, v_k, e_k)$ with all $e_i \\ni \\{v_i, v_{i+1}\\}$, where we take $v_{k+1}$ to be $v_1$.  Bohman, Frieze, and Mubayi proved that $\\chi &gt; 2rt$ is sufficient to embed every $r$-tree with $t$ edges, and asked whether the dependence on $r$ was necessary.  In this note, we completely solve their problem, proving the tight result that $\\chi &gt; t$ is sufficient to embed any $r$-tree with $t$ edges.<\/jats:p>","DOI":"10.37236\/256","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:29:17Z","timestamp":1578698957000},"source":"Crossref","is-referenced-by-count":5,"title":["A Note on Embedding Hypertrees"],"prefix":"10.37236","volume":"16","author":[{"given":"Po-Shen","family":"Loh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,6,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T21:53:03Z","timestamp":1579297983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/256","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,6,5]]},"article-number":"N18"}}