Constructing trees in graphs with no K2,s

Let s > 2 be an integer and k > 12(s - 1) an integer. We give a necessary and-sufficient condition for a graph G containing no K-2,K-s with S(G) >= k/2 and Delta(G) >= k to contain every tree T of order k + 1. We then show that every graph G with no K2,s and average degree greater than k- 1 satisfies this condition, improving a result of. Haxell, and verifying a special case of the Erdos-Sos conjecture, which states that every graph of average degree greater than k - 1 contains every tree of order k + 1. (c) 2007 Wiley Periodicals, Inc.