On the minimum number of empty polygons in planar point sets
Pável Valtr · Refubium (Universitätsbibliothek der Freien Universität Berlin) · 1992
We describe a configuration (related to Horton's constructions) of n points in general position in the plane with less than 1.8 n2 empty triangles less than 2.42 n2 empty quadrilaterals less than 1.46 n2 empty pentagons and less than n2/3 emptyhexagons. It improves the constants shown by Bárány and Füredi.