Existence of Almost Resolvable Directed 7-Cycle Systems

Let ARDkCS(v) denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS(v) is v≡1(mod k). For k= 3,4,5 and 6, the existence of an ARDkCS(v) had been completely solved. This paper shows that there exists an ARD7CS(v) if and only if v≡1(mod 7) and v≥8.