Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs

Grannell, M.J. and Korzhik, V.P. (2009). Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs. Discrete Mathematics, 309(9) pp. 2847–2860.

DOI: https://doi.org/10.1016/j.disc.2008.07.016

Abstract

We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n+1 rungs. Such an assignment yields an index one current graph with current group that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our characterization to construct Skolem sequences that give rise to such current assignments. These produce many nonisomorphic orientable biembeddings of cyclic Steiner triple systems of order 12n+7.

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