Cyclic biembeddings of twofold triple systems

Donovan, Diane M.; Griggs, Terry S.; Lefevre, James G. and McCourt, Thomas A. (2014). Cyclic biembeddings of twofold triple systems. Annals of Combinatorics, 18(1) pp. 57–74.

DOI: https://doi.org/10.1007/s00026-013-0211-8

Abstract

We construct face two-colourable triangulations of the graph 2K_n in an orientable surface; equivalently biembeddings of two twofold triple systems of order n, for all n ≡ 4 (mod 12). The biembeddings have a cyclic automorphism and the construction employs index 1 current graphs.

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