Abstract
For a positive integer k, a set of k + 1 vertices in a graph is a k-cluster if the difference between degrees of any two of its vertices is at most k − 1. Given any tree T with at least k3 edges, we show that for each graph G of sufficiently large order, either G or its complement contains a copy of T such that some vertices in the copy form a k-cluster in G. The same conclusion holds for any tree T having a vertex of degree more than k. © 1997 John Wiley & Sons, Inc.
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