Subgraph counts in random graphs using incomplete U-statistics methods
The random graph Kn,p is constructed on n labelled vertices by inserting each of the (n2) possible edges independently with probability p, 0> p < 1. For a fixed graph G, the threshold function for existence of a subgraph of Kn,p isomorphic to G has been determined by Erdös and Rényi [8] and Bollobás [3]. Bollobás [3] and Karo ski [14] have established asymptotic Poisson and normal convergence for