Spanning trees in random graphs

Abstract

For each $\Delta>0$, we prove that there exists some $C=C(\Delta)$ for which the binomial random graph $G(n,C\log n/n)$ almost surely contains a copy of every tree with $n$ vertices and maximum degree at most $\Delta$. In doing so, we confirm a conjecture by Kahn.Comment: 71 pages, 31 figures, version accepted for publication in Advances in Mathematic