Note On Forest Isomorphic Decomposition of Cayley Digraphs

We prove that if \(S\) is a quasiminimal generating set of a group \(\Gamma\) and \(F\) is an oriented forest with \(|S| > 2\) arcs, then the Cayley graph \({Cay}(\Gamma, S)\) can be decomposed into \(|\Gamma|\) arc-disjoint subdigraphs, each of which is isomorphic to \(F\).