The Erdos-Sos Conjecture for trees of diameter four

The Erdos-Sos Conjecture is that a finite graph G with average degree greater than k - 2 contains every tree with k vertices. Theorem 1 is a special case: every k-vertex tree of diameter four can be embedded in G. A more technical result, Theorem 2, is obtained by extending the main ideas in the proof of Theorem 1. (C) 2005 Wiley Periodicals, Inc.