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.



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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