On α-resolvable directed cycle systems for cycle length 4

A directedm-cycle system of order v with index λ, denotedm-DCS(v, λ), is a collection of directed cycles of length m whose directed edges partition the directed edges of λDKv. An m-DCS(v, λ) is α-resolvable if its directed cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m | αv and α | λ(v−1). It is shown in this paper that these conditions are also sufficient when m = 4, except for the case v = 4, λ ≡ 1 (mod 2).