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 \(F\).
Citation
A. Gutiérrez, A.S. Lladdt. Note On Forest Isomorphic Decomposition of Cayley Digraphs[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 041. 117-121. .