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.
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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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