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arXiv · 1410.1579

Counting Carambolas

Adrian Dumitrescu·Maarten Löffler·André Schulz·Csaba D. Tóth
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Abstract

We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \emph{convex polygons}, \emph{star-shaped polygons} and \emph{monotone paths}. We also consider related problems for \emph{directed} planar straight-line graphs.

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Adrian Dumitrescu, Maarten Löffler, André Schulz, Csaba D. Tóth. 2015-09-20. Counting Carambolas. https://doi.org/10.1007/s00373-015-1621-7

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