Asymptotically Optimal Tree-Packings in Regular Graphs

Let T be a tree with t vertices. Clearly, an n vertex graph contains at most n=t vertex disjoint trees isomorphic to T . In this paper we show that for every > 0, there exists a D(; t) > 0 such that, if d > D(; t) and G is a simple d-regular graph on n vertices, then G contains at least (1 )n=t vertex disjoint trees isomorphic to T .