On the orientable genus of the cartesian product of a complete regular tripartite graph with a even cycle

Abstract

We apply the technique of patchwork embeddings to find orientable genus embeddings of the Cartesian product of a complete regular tripartite graph with a even cycle. In particular, the orientable genus of kc is determined for mge1 and for all nge3 and n=1. For $n= 2 both lower and upper bounds are given. we see that the resulting embeddings may have a mixture of triangular and quadrilateral faces, in contrast to previous applications of patchwork method.