On the Erdos-Sos conjecture

Erdos and Sos conjectured in 1963 that if G is a graph of order n and size e(G) with e(G) 1/2 n(k - 1), then G contains every tree T of size k. We present some partial results; in particular the proof of the conjecture in the case k = n - 3 (C) 1996 John Wiley & Sons, Inc.