Distribution of subgraphs of random regular graphs
We obtain the asymptotic distribution of the number of copies of a fixed subgraph H in a random d-regular graph, provided H is strictly balanced and d = d(n) is chosen so that the expected number of copies of H tends to infinity (but not too quickly), and the expected number of copies sharing edges with two other copies is bounded. The proof of asymptotic normality of the distribution uses a method of factorial moments for variables with unbounded means that was recently derived by the authors. (c) 2007 Wiley Periodicals, Inc.
subgraphs random regular graphs moments normal distribution