English

Globally simple Heffter arrays and orthogonal cyclic cycle decompositions

Combinatorics 2018-06-13 v2

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 k10k\leq 10. Furthermore, starting from our Heffter arrays we also obtain biembeddings of two kk-cycle decompositions on orientable surfaces.

Keywords

Cite

@article{arxiv.1709.05812,
  title  = {Globally simple Heffter arrays and orthogonal cyclic cycle decompositions},
  author = {Simone Costa and Fiorenza Morini and Anita Pasotti and Marco Antonio Pellegrini},
  journal= {arXiv preprint arXiv:1709.05812},
  year   = {2018}
}

Comments

The present version also considers the problem of biembeddings