Minimum degree and minimum number of edge-disjoint trees Original Research Article

A tree decomposition of a graph G is a family of subtrees whose sets of edges partition the set of edges of G. The arboricity is a trivial lower bound for the minimum number, τ(G), of trees in a tree decomposition of G. We prove that a(G)=τ(G) for all graphs with minimum degree δ⩾⌊n/2⌋ and order n. The bound on the minimum degree is best possible.