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arXiv · 1505.04070

Biembedding Steiner Triple Systems and n-cycle Systems on Orientable Surfaces

Jeffrey H. Dinitz·Amelia R. W. Mattern
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Abstract

In 2015, Archdeacon introduced the notion of Heffter arrays and showed the connection between Heffter arrays and biembedding m-cycle and an n-cycle systems on a surface. In this paper we exploit this connection and prove that for every n >= 3 there exists an orientable embedding of the complete graph on 6n+1 vertices with each edge on both a 3-cycle and an $n$-cycle. We also give an analogous (but partial) result for biembedding a 5-cycle system and an n-cycle system.

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Jeffrey H. Dinitz, Amelia R. W. Mattern. 2015-05-15. Biembedding Steiner Triple Systems and n-cycle Systems on Orientable Surfaces. https://arxiv.org/abs/1505.04070

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