On the decomposition of n-cubes into isomorphic trees

We prove that if T is any tree having n edges (n ≥ 1), then the n-cube Q_n can be decomposed into 2^n-1 edge-disjoint induced subgraphs, each of which is isomorphic to T. We use this statement to obtain two results concerning decompositions of Q_n into subgraphs isomorphic to members of a specified family of trees.