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

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 .