Induced Forests and Trees in Erdős–Rényi Random Graph

Abstract

We prove that the size of the maximum induced forest (of bounded and unbounded degree) in the binomial random graph \(G(n,p)\) for \({{C}_{\varepsilon }}{\text{/}}n < p < 1 - \varepsilon \) with an arbitrary fixed \(\varepsilon > 0\) is concentrated in an interval of size \(o(1{\text{/}}p)\). We also show 2-point concentration for the size of the maximum induced forest (and tree) of bounded degree in \(G(n,p)\) for p = const.