| 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
determined for $m ge 1$ and for all $n ge 3$ 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.
Graph Embeddings, Genus, Cartesian Product, Patchworks
Math Review Classification
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