Solitary subgraphs of random graphs Original Research Article

Let G be a graph and let G(n,p) be the binomial random graph with n vertices and edge probability p. We consider copies of G in G(n,p), vertex disjoint from all other such copies. For a strictly balanced graph G, initially, every copy of G in G(n,p) is solitary. Suen (Random Struct. Algorithms 1 (1990) 231–242) established a second (disappearance) threshold for a subclass of strictly balanced graphs. In this paper we extend his result to a more general case.