Another kind of flip graphs is obtained by considering the triangulations of a topological surface: consider such a surface \mathcal{S}, place a finite number n of points on it, and connect them by arcs in such a way that any two arcs never cross. When this set of arcs is maximal, it decomposes \mathcal{S} into triangles. If in addition there are no multiple arcs (distinct arcs with the same pair of vertices), nor loops, this set of arcs defines a triangulation of \mathcal{S}.
