Sieve Methods in Random Graph Theory

We apply the Tur\´an sieve and the simple sieve developed by Ram Murty and Yu-Ru Liu to study problems in random graph theory. More specifically, we obtain bounds on the probability of a graph having diameter 2 (or diameter 3 in the case of bipartite graphs). An interesting feature revealed in these results is that the Tur´an sieve and the simple sieve “almost completely” complement to each other. This is joint work with Yu-Ru Liu.