Diagonal flips in outer-torus triangulations (Q1567266)

An outer-torus triangulation is introduced as a triangulation of a simple graph on the torus such that there exists a face on whose boundary each of its vertices appears exactly once. Then, the authors show that for any two outer-torus triangulations \(T_1\) and \(T_2\), there exists a sequence of diagonal flips by which \(T_1\) can be transformed into another which is homeomorphic to \(T_2\). This is analogous to the well-known planar case.