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Grannell, Mike and Griggs, Terry
(2007).
Abstract
An embedding of a graph in a surface gives rise to a combinatorial design whose blocks correspond to the faces of the embedding. Particularly interesting graphs include complete and complete multipartite graphs. Embeddings of these in which the faces are triangles, Hamiltonian cycles, or Eulerian cycles generate interesting designs. These designs include twofold, Mendelsohn and Steiner triple systems, and Latin squares. We examine some of these cases, looking at construction methods, structural properties and enumeration problems.