The Erdos-Sos conjecture for spiders of large size

The Erdos-Sos Conjecture states that if G is a graph with average degree more than k - 1, then G contains every tree with k edges. A spider is a tree with at most one vertex of degree more than 2. In this paper, we prove that if G is a graph on n vertices with average degree more than k - 1, then G contains every spider with k edges, where k >= n+5/2. (C) 2013 Elsevier B.V. All rights reserved.