Computational Geometry pp 138-145

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579) | Cite as

Simultaneously Flippable Edges in Triangulations

  • Diane L. Souvaine
  • Csaba D. Tóth
  • Andrew Winslow

Abstract

Given a straight-line triangulation T, an edge e in T is flippable if e is adjacent to two triangles that form a convex quadrilateral. A set of edges E in T is simultaneously flippable if each edge is flippable and no two edges are adjacent to a common triangle. Intuitively, an edge is flippable if it may be replaced with the other diagonal of its quadrilateral without creating edge-edge intersections, and a set of edges is simultaneously flippable if they may be all be flipped without interferring with each other. We show that every straight-line triangulation on n vertices contains at least (n − 4)/5 simultaneously flippable edges. This bound is the best possible, and resolves an open problem by Galtier et al.

Keywords

planar graph graph transformation geometry combinatorics 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Diane L. Souvaine
    • 1
  • Csaba D. Tóth
    • 2
  • Andrew Winslow
    • 1
  1. 1.Tufts UniversityMedfordUSA
  2. 2.University of CalgaryCalgaryCanada

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