, Volume 19, Issue 2, pp 267-296

Mangoes and Blueberries

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Dedicated to the memory of Paul Erdős

We prove the following conjecture of Erdős and Hajnal:

For every integer k there is an f(k) such that if for a graph G, every subgraph H of G has a stable set containing vertices, then G contains a set X of at most f(k) vertices such that GX is bipartite.

This conjecture was related to me by Paul Erdős at a conference held in Annecy during July of 1996. I regret not being able to share the answer with him.

Received: August 20, 1997