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

Craig Paul Bonnington, Tomaz Pisanski

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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 Km,m,m ?? C2n is determined for m a?Y 1 and for all n a?Y 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 the patchwork method.
Original languageEnglish
Pages (from-to)301 - 307
Number of pages7
JournalArs Combinatoria
Volume70
Publication statusPublished - 2004

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