Sharp threshold functions via a coupling method

Abstract

We will present a new method used to establish threshold functions in the random intersection graph model. The method relies on a coupling of a random intersection graph with a random graph similar to an Erdős and Rényi random graph. Formerly a simple version of the technique was used in the case of homogeneous random intersection graphs. Now it is considerably modified and extended in order to be applied in the general case. By means of the method we are able to establish threshold functions for the general random intersection graph model for monotone properties. Moreover the new approach allows to sharpen considerably the best known results concerning threshold functions for homogeneous random intersection graph. We outline the main results obtained in [10].