{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:48Z","timestamp":1753893768750,"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>Let $N=\\binom{n}{2}$ and $s\\geq 2$. Let $e_{i,j},\\,i=1,2,\\ldots,N,\\,j=1,2,\\ldots,s$ be $s$ independent permutations of the edges $E(K_n)$ of the complete graph $K_n$. A MultiTree is a set $I\\subseteq [N]$ such that the edge sets $E_{I,j}$ induce spanning trees for $j=1,2,\\ldots,s$. In this paper we study the following question: what is the smallest $m=m(n)$ such that w.h.p. $[m]$ contains a MultiTree. We prove a hitting time result for $s=2$ and an $O(n\\log n)$ bound for $s\\geq 3$.<\/jats:p>","DOI":"10.37236\/10804","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T17:06:17Z","timestamp":1675962377000},"source":"Crossref","is-referenced-by-count":0,"title":["Multitrees in Random Graphs"],"prefix":"10.37236","volume":"30","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wesley","family":"Pegden","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,2,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T17:06:17Z","timestamp":1675962377000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i1p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/10804","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,2,10]]},"article-number":"P1.30"}}