Abstract.
A classical result of Wagner states that any two (unlabelled) planar triangulations with the same number of vertices can be transformed into each other by a finite sequence of diagonal flips. Recently Komuro gives a linear bound on the maximum number of diagonal flips needed for such a transformation. In this paper we show that any two labelled triangulations can be transformed into each other using at most O(nlogn) diagonal flips. We will also show that any planar triangulation with n>4 vertices has at least n− 2 flippable edges. Finally, we prove that if the minimum degree of a triangulation is at least 4, then it contains at least 2n + 3 flippable edges. These bounds can be achieved by an infinite class of triangulations.
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Received: June 3, 1998 Final version received: January 26, 2001
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Gao, Z., Urrutia, J. & Wang, J. Diagonal Flips in Labelled Planar Triangulations. Graphs Comb 17, 647–657 (2001). https://doi.org/10.1007/s003730170006
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DOI: https://doi.org/10.1007/s003730170006