Poisson Approximation for the Number of Induced Copies of a Fixed Graph in a Random Regular Graph

Abstract

Let G n,d be a random d-regular graph with n vertices. Given a fixed graph H. W denotes the number of induced copies of H in G n,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.

POISSON APPROXIMATION FOR THE NUMBER OF OPIES OF A FIXED GRAPH IN A RANDOM d-REGULAR GRAPH

“…In this work, we use the Stein-Chen and Coupling method to approximate W , the number of copies of H in G n,d , and show that the error term of this approximation is better than that of Mana Donganont and Angkana Boonyued [9]. The result as following.…”

“…e → c for some positive constant c, then W converges to P oi λ , the Poisson distribution with mean λ = c e Aut(H) . Next, in 2010, Mana Donganont and Angkana Boonyued [9] showed that the distribution function of W can be approximate by Poisson distribution and the error term of this approximation by using Stein-Chen method and Local approach the result as following.…”

“…Theorem 1.2. [9] Let H be a fixed graph with v H vertices and e H ≥ v H edges and let W be the number of copies of…”