Globally simple Heffter arrays and orthogonal cyclic cycle decompositions

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 $k\le 10$. Furthermore, starting from our Heffter arrays we also obtain biembeddings of two $k$-cycle decompositions on orientable surfaces.

The present version also considers the problem of biembeddings

References in corpus (1)

• On Partial Sums in Cyclic Groups

Cited by in corpus (5)

• On $\lambda$-fold relative Heffter arrays and biembedding multigraphs on surfaces
• Constructing generalized Heffter arrays via near alternating sign matrices
• Globally simple Heffter arrays $H(n;k)$ when $k\equiv 0,3\mathrm{mod}4$
• Biembeddings of cycle systems using integer Heffter arrays
• The existence of square non-integer Heffter arrays