Poisson approximation of counts of induced subgraphs in random intersection graphs

Random intersection graphs are characterised by three parameters: n, m and p, where n is the number of vertices, m is the number of objects, and p is the probability that a given object is associated with a given vertex. Two vertices in a random intersection graph are adjacent if and only if they have an associated object in common. When m=⌊nα⌋ for constant α, we provide a condition, called strictly α-balanced, for the Poisson convergence of the number of induced copies of a fixed subgraph.