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 Cε/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 Cε/n<p<1−ε. Presumably, it is the first generalization of Frieze's result to another class of induced subgraphs for such a range of p.