Graph of triangulations of a convex polygon and tree of triangulations

Abstract 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 we introduce 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.

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