论文信息 - PLANAR POINT SETS WITH A SMALL NUMBER OF EMPTY CONVEX POLYGONS

PLANAR POINT SETS WITH A SMALL NUMBER OF EMPTY CONVEX POLYGONS

A subset A of a finite set P of points in the plane is called an empty polygon, if each point of A is a vertex of the convex hull of A and the convex hull of A contains no other points of P . We construct a set of n points in general position in the plane with only ≈ 1.62n empty triangles, ≈ 1.94n empty quadrilaterals, ≈ 1.02n empty pentagons, and ≈ 0.2n empty hexagons.

G. Fejes Tóth

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