On Circular 2-Factorizations of the Complete Tripartite Graph

We consider 2-factorizations of the complete tripartite graph K{n;3) where each 2-factor consists of cycles with even length. An additional requirement is related to pairs of edges being consecutive in an arbitrary cycle. For all pairs of edges we require that the three nodes incident to these two edges must be from different partite sets of the tripartite graph. We show that such a 2-factorizations cannot exist if n = 2 or n is odd. Furthermore, we show how to construct such a 2-factorization for all even n with n{2,26,34,58,74}.