Convex Polygons in Geometric Triangulations

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

Abstract

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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