Abstract
We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029n). This improves an earlier bound of O(1.6181n) established by van Kreveld, Löffler, and Pach (2012) and almost matches the current best lower bound of Ω(1.5028n) 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.
Cite
CITATION STYLE
Dumitrescu, A., & Tóth, C. D. (2015). Convex polygons in geometric triangulations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9214, pp. 289–300). Springer Verlag. https://doi.org/10.1007/978-3-319-21840-3_24
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