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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Dumitrescu, A., Tóth, C.D. (2015). Convex Polygons in Geometric Triangulations. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_24
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DOI: https://doi.org/10.1007/978-3-319-21840-3_24
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