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

Costa, S., Morini, F., Pasotti, A., Pellegrini, M. A., Globally simple heffter arrays and orthogonal cyclic cycle decompositions, <<THE AUSTRALASIAN JOURNAL OF COMBINATORICS>>, 2018; 72 (3): 549-593 [http://hdl.handle.net/10807/126610]

Globally simple heffter arrays and orthogonal cyclic cycle decompositions

Pellegrini, Marco Antonio
Ultimo
2018

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 ≤ 10. Furthermore, starting from our Heffter arrays we also obtain biembeddings of two k-cycle decompositions on orientable surfaces.
2018
Inglese
Costa, S., Morini, F., Pasotti, A., Pellegrini, M. A., Globally simple heffter arrays and orthogonal cyclic cycle decompositions, <<THE AUSTRALASIAN JOURNAL OF COMBINATORICS>>, 2018; 72 (3): 549-593 [http://hdl.handle.net/10807/126610]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/126610
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