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

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