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.

Globally simple Heffter arrays and orthogonal cyclic cycle decompositions / Costa, Simone; Morini, Fiorenza; Pasotti, Anita; Antonio Pellegrini, Marco. - In: THE AUSTRALASIAN JOURNAL OF COMBINATORICS. - ISSN 2202-3518. - 72:3(2018), pp. 549-593.

### 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 $k\leq 10$. Furthermore, starting from our Heffter arrays we also obtain biembeddings of two $k$-cycle decompositions on orientable surfaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2850524
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