### 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 language | English |
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Pages (from-to) | 301 - 307 |

Number of pages | 7 |

Journal | Ars Combinatoria |

Volume | 70 |

Publication status | Published - 2004 |

## Cite this

Bonnington, C. P., & Pisanski, T. (2004). On the orientable genus of the cartesian product of a complete regular tripartite graph with an even cycle.

*Ars Combinatoria*,*70*, 301 - 307.