Spanning trees in the square of pseudorandom graphs

Abstract

We show that for every $\Delta \in \mathbb{N}$, there exists a constant $C$ such that if $G$ is an $(n,d,\lambda )$-graph with $d/\lambda \ge C$ and $d$ is large enough, then $G^2$ contains every $n$-vertex tree with maximum degree bounded by $\Delta$. This answers a question of Krivelevich.

A slightly more general result is added