On cyclic GG-designs where GG is a cubic tripartite graph

It is known that a ρρ-tripartite labeling of a tripartite graph GG with nn edges can be used to obtain a cyclic GG-decomposition of K2nt+1K2nt+1 for every positive integer tt. We show that if GG is an odd prism, an even Möbius ladder or a connected cubic tripartite graph of order at most 10, then GG admits a ρρ-tripartite labeling. We conjecture that every connected tripartite cubic graph admits a ρρ-tripartite labeling.