Note On Forest Isomorphic Decomposition of Cayley Digraphs

Abstract

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