A generalization of diagonal flips in a convex polygon

摘要

A diagonal flip is an operation that converts one triangulation of a convex polygon into another. in this paper we generalize this operation to prove some results including the next theorem. Theorem. Let E-1 and E-2 be any two sets of edges in a convex polygon such that each Ei has no t + 1 pairwise crossing edges and E-i U {e} contains t + 1 pairwise crossing edges for any edge e is not an element of E-i. Then, E-1 can be transformed into E-2 by a sequence of diagonal flips such that each flip changes one edge to another preserving the above property. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 7]