Burning Random Trees

Let T be a Galton-Watson tree with a given offspring distribution ξ, where ξ is a Z≥ 0-valued random variable with E[ξ] = 1 and 0 < σ²:=Var[ξ] < ∞. For n ≥ 1, let Tₙ be the tree T conditioned to have n vertices. In this paper we investigate b(Tₙ), the burning number of Tₙ. Our main result shows that asymptotically almost surely b(Tₙ) is of the order of n1/3.