Poisson approximation of the number of triangles in random intersection graphs

An intersection graph is constructed from a set of vertices and an auxiliary set of objects by assigning subsets of the objects to the vertices and connecting two vertices if their object sets are not disjoint. In a random intersection graph G(n,m,p) there are n vertices, m objects and each object is in the object set of each vertex independently and with probability p. We use Stein's method to approximate the distribution of triangles in G(n,m,p) by a Poisson distribution.