Document Type thesis Author Name Potter, John R URN etd-021408-102227 Title Pseudo-Triangulations On Closed Surfaces Degree MS Department Mathematical Sciences Advisors Brigitte Servatius, Advisor Keywords Embeddings Graph Theory Pseudo-Triangulations Date of Presentation/Defense 2007-12-12 Availability unrestricted
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.
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