On resolvable tree-decompositions of complete graphs

A partition of the edge set of a graph H into subsets inducing graphs H₁,…,H_s isomorphic to a graph G is said to be a G-decomposition of H. A G-decomposition of H is resolvable if the set {H₁,…,H_s} can be partitioned into subsets, called resolution classes, such that each vertex of H occurs precisely once in each resolution class. We prove that for every graceful tree T of odd order the obvious necessary conditions for the existence of a resolvable T-decomposition of a complete graph are asymptotically sufficient. This generalizes the results of Horton and Huang concerning paths and stars.