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On the minimum number of empty polygons in planar point sets

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

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Server: fubinf.inf.fu-berlin.de
File: pub/reports/tr-b-92-01.ps.gz

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.