Tree decomposition of graphs

Abstract

Let H be a tree on h≥2 vertices. It is shown that if G=(V, E) is a graph with \delta (G)\ge (|V|/2)+10h^4\sqrt{|V|\log|V|}, and h−1 divides |E|, then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 237–251, 1998