The Directed Uniform Hamilton-Waterloo Problem Involving Even Cycle Sizes

In this paper, factorizations of the complete symmetric digraph \(K_v^*\) into uniform factors consisting of directed even cycle factors are studied as a generalization of the undirected Hamilton-Waterloo Problem. It is shown, with a few possible exceptions, that \(K_v^*\) can be factorized into two nonisomorphic factors, where these factors are uniform factors of \(K_v^*\) involving \(K_2^*\) or directed \(m\)-cycles, and directed \(m\)-cycles or \(2m\)-cycles for even \(m\).