A lower bound for the number of orientable triangular embeddings of some complete graphs

Grannell, M. J. and Knor, M. (2010). A lower bound for the number of orientable triangular embeddings of some complete graphs. Journal of Combinatorial Theory, Series B, 100(2) pp. 216–225.

DOI: https://doi.org/10.1016/j.jctb.2009.08.001

Abstract

We prove that, for a certain positive constant a and for an infinite set of values of n, the number of nonisomorphic face 2-colourable triangular embeddings of the complete graph Kn in an orientable surface is at least nan2.

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