On the number of distinct spanning trees in pseudorandom graphs

Abstract

A celebrated result of Otter says the number of distinct unlabelled spanning trees in $K_n$ is $α^n$ up to subexponential factors for an absolute constant $α>0$. In this note, we prove that for every $0<\varepsilon<α$, there are constants $C$ and $d_0$ such that every $(n,d,λ)$-graph with $d\geq d_0$ and $d/λ\geq C$ has at least $(α-\varepsilon)^n$ distinct unlabelled spanning trees.