The maximum size of an induced forest in the binomial random graph

Abstract

The celebrated Frieze's result about the independence number of $G(n,p)$ states that it is concentrated in an interval of size $o(1/p)$ for all $C_{\epsilon }/n<p=o(1)$. We show concentration in an interval of size $o(1/p)$ for the maximum size (number of vertices) of an induced forest in $G(n,p)$ for all $C_{\epsilon }/n<p<1-\epsilon$. Presumably, it is the first generalization of Frieze's result to another class of induced subgraphs for such a range of $p$.