The maximum degree of the $r$th power of a sparse random graph

Alan Frieze, Aditya Raut

Let $G_{n,p}^r$ denote the $r$th power of the random graph $G_{n,p}$, where $p=c/n$ for a positive constant $c$. We prove that w.h.p. the maximum degree $Δ\left(G^r_{n,p}\right)\si…