Some Properties of the Genelized Ramsey Number p(n,k)

Let n,k≥3 be positive integers, and let p(n,k) be the smallest natural number p such that for every graph G of order p, either G has an induced subgraph with n vertices and at least n-1 edges, or G has an independent set with k vertices. In the paper we prove that p(n,k)≥max{p(n,k-1),p(n-1,k)}, and that p(n,k)≥2k-2+n3 provided n3k-4, where is the greatest integer function.