2p-cycle decompositions of some regular graphs and digraphs

In this paper, we consider 2k-cycle decomposition of Km×Kn and directed 2k-cycle decompositions of (Km∘K¯n)∗ and (Km×Kn)∗, where ∘ and × denote the wreath product and tensor product of graphs, respectively. Using the results obtained here, we prove that for m,n≥3, the obvious necessary conditions for the existence of a C2k-decomposition of Km×Kn are sufficient whenever k∈{p,2ℓ}, where p is a prime and ℓ≥2. Also, we show that the necessary conditions for the existence of C→2p-decompositions of (Km∘K¯n)∗ and (Km×Kn)∗ are sufficient whenever p is a prime, where C→2p denotes the directed cycle of length 2p.