Embeddings and designs

Grannell, Mike and Griggs, Terry (2009). Embeddings and designs. In: Wilson, Robin and Beineke, LW eds. Topics in Topological Graph Theory. Cambridge: Cambridge University Press, pp. 268–288.

Abstract

When a graph is embedded in a surface, the faces that result can be regarded as the blocks of a combinatorial design. The resulting design may be thought of as being embedded in the surface. This perspective leads naturally to a number of fascinating questions about embeddings, in particular about embeddings of Steiner triple systems and related designs. Can every Steiner triple system be embedded, can every pair of Steiner triple systems be biembedded, and how many embeddings are there of a given type?

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