Compatible Hamilton decompositions of directed wrapped butterfly graphs

In this article we prove a conjecture of Bermond, Darrot, Delmas, and Perennes by constructing a Hamilton decomposition of the directed wrapped butterfly graph W &Brarr;F(p,2), where p is a prime greater than 3. This, together with results of Bermond et al., completes the proof that W &Brarr;F(d,n) has a Hamilton decomposition for all d and n. We then construct p − 2 pairwise compatible Hamilton decompositions of W &Brarr;F(p,2).