Cyclic Uniform 2-Factorizations of the Complete Multipartite Graph

A generalization of the Oberwolfach problem, proposed by Liu (J Comb Des 8:42–49, 2000), asks for a uniform 2-factorization of the complete multipartite graph Km×n. Here we focus our attention on cyclic 2-factorizations, whose 2-factors are disjoint union of cycles all of even length l. In particular, we present a complete solution for the extremal cases l=4 and l=mn.