Graph Theory and Probability. II

Abstract

Define f(k, l) as the least integer so t h a t every graph having f(k, l) vertices contains either a complete graph of order k or a set of l independent vertices (a complete graph of order k is a graph of k vertices every two of which are connected by an edge, a set of I vertices is called independent if no two are connected by an edge). Throughout this paper c 1 , c 2 , … will denote positive absolute constants. It is known (1, 2) that (1) and in a previous paper (3) I stated that I can prove that for every ∈ > 0 and l > l(∈), f (3, l) > l 2-∈ . In the present paper I am going to prove that (2)