Transforming Triangulations on Nonplanar Surfaces
Carmen Cortés, Clara I. Grima, F. Hurtado, Alberto Márquez, Francisco Santos, J. Valenzuela · SIAM Journal on Discrete Mathematics · 2010
We consider whether any two triangulations of a polygon or a point set on a nonplanar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder.