Almost Resolvable Directed $m$-cycle systems: $m\equiv 3(mod6)$

Abstract

Let $m\equiv 3(\mathrm{mod}6)$. We show that there exists an almost resolvable directed $m$-cycle system of $D_n$ if and only if $n\equiv 1(\mathrm{mod}m)$, except possibly if $n\in \{3m+1,6m+1\}$.