Diagonal flips in outer-torus triangulations Original Research Article

An outer-torus triangulation G with n vertices is a fixed embedding of a simple graph on the torus such that there is one face bounded by a cycle of length n and other faces are all triangular. We show that any two outer-torus triangulations with the same number of vertices can be transformed into each other by a sequence of diagonal flips, through outer-torus triangulations, up to homeomorphism.