Shifting attention from the plane to the sphere and torus, we extend the study of pseudo-triangulations. Planar representations of each surface are used. A number of theorems and concepts are taken from the plane and applied to the sphere and torus not only for pseudo-triangulations but for triangulations as well. We found the number of edges and faces in a triangulation on n vertices in the plane, on the sphere and on the torus.
Worcester Polytechnic Institute
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Potter, John R., "Pseudo-Triangulations On Closed Surfaces" (2008). Masters Theses (All Theses, All Years). 163.
Embeddings, Graph Theory, Pseudo-Triangulations, Triangulation, Graph theory, Embeddings (Mathematics)