{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819492,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a fixed graph $H$ with $t$ vertices, an $H$-factor of a graph $G$ with $n$ vertices, where $t$ divides $n$, is a collection of vertex disjoint (not necessarily induced) copies of $H$ in $G$ covering all vertices of $G$. We prove that for a fixed tree $T$ on $t$ vertices and $\\epsilon&gt;0$, the random graph $G_{n,p}$, with $n$ a multiple of $t$, with high probability contains a family of edge-disjoint $T$-factors covering all but an $\\epsilon$-fraction of its edges, as long as $\\epsilon^4 n p \\gg \\log^2 n$. Assuming stronger divisibility conditions, the edge probability can be taken down to $p&gt;\\frac{C\\log n}{n}$. A similar packing result is proved also for pseudo-random graphs, defined in terms of their degrees and co-degrees.<\/jats:p>","DOI":"10.37236\/3285","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:06:19Z","timestamp":1578704779000},"source":"Crossref","is-referenced-by-count":1,"title":["Packing Tree Factors in Random and Pseudo-Random Graphs"],"prefix":"10.37236","volume":"21","author":[{"given":"Deepak","family":"Bal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Krivelevich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Po-Shen","family":"Loh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2014,4,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:00:27Z","timestamp":1579258827000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i2p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/3285","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,4,16]]},"article-number":"P2.8"}}