Mangoes and blueberries

We prove the following conjecture of Erdos and Hajnal: For every integer k there is an f(k) such that if for a graph G, every subg raph H of G has a stable set containing \V(H)\-k/2 vertices, then G contain s a set X of at most f(k) vertices such that G-X is bipartite. This conjecture was related to me by Paul Erdos at a conference held in Ann ecy during July of 1996. I regret not being able to share the answer with h im.