Expanding graphs contain all small trees
Combinatorica
Journal of Combinatorial Theory Series A
Spanning Trees in Dense Graphs
Combinatorics, Probability and Computing
Journal of Graph Theory
Random Structures & Algorithms
Embedding nearly-spanning bounded degree trees
Combinatorica
Local resilience of almost spanning trees in random graphs
Random Structures & Algorithms
Expanders are universal for the class of all spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast embedding of spanning trees in biased Maker-Breaker games
European Journal of Combinatorics
Sharp threshold for the appearance of certain spanning trees in random graphs
Random Structures & Algorithms
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We prove that if $T$ is a tree on $n$ vertices with maximum degree $\Delta$ and the edge probability $p(n)$ satisfies $np\geq C\max\{\Delta\log n,n^{\epsilon}\}$ for some constant $\epsilon0$, then with high probability the random graph $G(n,p)$ contains a copy of $T$. The obtained bound on the edge probability is shown to be essentially tight for $\Delta=n^{\Theta(1)}$.