Convex Polygons in Geometric Triangulations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)


We show that the maximum number of convex polygons in a triangulation of n points in the plane is \(O(1.5029^n)\). This improves an earlier bound of \(O(1.6181^n)\) established by van Kreveld, Löffler, and Pach (2012) and almost matches the current best lower bound of \(\Omega (1.5028^n)\) due to the same authors. We show how to compute efficiently the number of convex polygons in a given a planar straight-line graph with n vertices.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of Wisconsin–MilwaukeeMilwaukeeUSA
  2. 2.California State University NorthridgeLos AngelesUSA
  3. 3.Tufts UniversityMedfordUSA

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