Small surface trades in triangular embeddings

Bennett, G. K.; Grannell, M. J.; Griggs, T. S. and Siran, J. (2006). Small surface trades in triangular embeddings. Discrete Mathematics, 306(21) pp. 2637–2646.

DOI: https://doi.org/10.1016/j.disc.2006.04.027

Abstract

We enumerate all possible trades which involve up to six faces of the face set of a triangular embedding of a simple connected graph. These are classified by the underlying combinatorial trade on the associated block design, and by the geometrical arrangement of the faces necessary to avoid creation of a pseudosurface in the trading operation. The relationship of each of these trades to surface orientability is also established.

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