Counting Carambolas

Adrian Dumitrescu , Maarten L\"offler , Andr\'e Schulz , Csaba D. T\'oth

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classification 🧮 math.CO cs.DM

keywords emphconfigurationspolygonsboundscarambolasconsiderconvexcounting

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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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Counting Carambolas

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