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Abstract. In this paper we study the problem of flipping edges in triangulations of polygons and point sets. One of the main results is that any triangulation of a set of n points in general position contains at least (n − 4)/2 edges that can be flipped. We also prove that O(n + k 2 ) flips are sufficient to transform any triangulation of an n-gon with k reflex vertices into any other triangulation. We produce examples of n-gons with triangulations T and T such that to transform T into T requires (n 2 ) flips. Finally we show that if a set of n points has k convex layers, then any triangulation of the point set can be transformed into any other triangulation using at most O(kn) flips.

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