Planar point sets with a small number of empty convex polygons
Imre Bárány, Pável Valtr · Studia Scientiarum Mathematicarum Hungarica · 2004
A subsetAof a finite setPof points in the plane is called anempty polygon, if each point ofAis a vertex of the convex hull ofAand the convex hull ofAcontains no other points ofP. We construct a set ofnpoints in general position in the plane with only ˜1.62n2empty triangles, ˜1.94n2empty quadrilaterals, ˜1.02n2empty pentagons, and ˜0.2n2empty hexagons.