On the minimum number of empty polygons in planar point sets

Pavel Valtr Institut für Informatik Freie Universität Berlin Report B 92-01 January 1992

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We describe a configuration (related to Horton's constructions) of n points in general position in the plane with less than $1.8 n^2$ empty triangles, less than $2.42 n^2$ empty quadrilaterals, less than $1.46 n^2$ empty pentagons, and less than n 2/3 empty hexagons. It improves the constants shown by Bárány and Füredi.