Poisson approximation for the number of induced copies of a fixed graph in a random regular graph

Abstract

Let Gn,dbe a random d-regular graph with n vertices. Given a fixed graph H. W denotes the number of induced copies of H in Gn,d. In this paper, we use Stein-Chen method and Local approach to show that W can approximate by the Poisson distribution and give the bound of this approximation.