Abstract: | We consider non-overlapping subgraphs of fixed order in the random graph Kn, p(n). Fix a strictly strongly balanced graph G. A subgraph of Kn, p(n) isomorphic to G is called a G-subgraph. Let Xn be the number of G-subgraphs of Kn, p(n) vertex disjoint to all other G-subgraphs. We show that if EXn]→∞ as n→, then Xn/EXn] converges to 1 in probability. Also, if EXn]→c as n→∞, then Xn satisfies a Poisson limit theorem. the Poisson limit theorem is shown using a correlation inequality similar to those appeared in Janson, ?uczak, and Ruciñski8] and Boppana and Spencer 4]. |