On the decomposition of Cayley color graphs into isomorphic oriented trees (Q1328386)

Let \(\Delta\) be a minimal generating set for a nontrivial group \(\Gamma\) and \(T\) be an oriented tree with \(| \Delta|\) edges. It is shown that the Cayley color graph \(D_ \Delta(\Gamma)\) can be decomposed into \(|\Gamma|\) edge-disjoint subgraphs, each isomorphic to \(T\). An extension to \(H\)-decompositions of Cayley graphs for weakly connected oriented graphs \(H\), and results about decompositions of Cayley color graphs into prescribed families of oriented trees, are obtained. Applications to decompositions of the \(n\)-dimensional hypercube \(Q_ n\) are discussed.