Graph of triangulations of a convex polygon and tree of triangulations
Define a graph \(G_T(n)\) with one node for each triangulation of a convex \(n\)-gon. Place an edge between each pair of nodes that differ by a single flip: two triangles forming a quadrilateral are exchanged for the other pair of triangles forming the same quadrilateral. In this paper there is introduced a tree of all triangulations of polygons with any number of vertices which gives a unified framework in which several results on \(G_T(n)\) admit new and simple proofs.
scientific article; zbMATH DE number 1389795