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arXiv · 1709.05812

Globally simple Heffter arrays and orthogonal cyclic cycle decompositions

Simone Costa·Fiorenza Morini·Anita Pasotti·Marco Antonio Pellegrini
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Abstract

In this paper we introduce a particular class of Heffter arrays, called globally simple Heffter arrays, whose existence gives at once orthogonal cyclic cycle decompositions of the complete graph and of the cocktail party graph. In particular we provide explicit constructions of such decompositions for cycles of length $k\leq 10$. Furthermore, starting from our Heffter arrays we also obtain biembeddings of two $k$-cycle decompositions on orientable surfaces.

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Simone Costa, Fiorenza Morini, Anita Pasotti, Marco Antonio Pellegrini. 2018-06-12. Globally simple Heffter arrays and orthogonal cyclic cycle decompositions. https://arxiv.org/abs/1709.05812

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