Globally simple Heffter arrays and orthogonal cyclic cycle decompositions

2017/09/18 by Simone Costa, Costa, Simone, Fiorenza Morini +5 · 1 citation
Computer Science · Decision Sciences · Engineering · #05B20 #05B30 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Optimal Experimental Design Methods #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1709.05812

openalex publication_date 2017/09/18 · openalex created_date 2017/09/25 · openalex updated_date 2026/07/28

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.

Citations

• On Partial Sums in Cyclic Groups

Cited by

• Globally Simple Heffter Arrays H(n;k) with k ≡ 1 \pmod4

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