Abstract:Counting interior-disjoint empty convex polygons in a point set is a typical Erdős-Szekerestype problem. We study this problem for 4-gons. Let P be a set of n points in the plane and in general position. A subset Q of P , with four points, is called a 4-hole in P if Q is in convex position and its convex hull does not contain any point of P in its interior. Two 4-holes in P are compatible if their interiors are disjoint. We show that P contains at least 5n/11 −1 pairwise compatible 4-holes. This improves the l… Show more
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