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  • Author or Editor: Pavel Valtr x
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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 2 empty triangles, ˜1.94n 2 empty quadrilaterals, ˜1.02n 2 empty pentagons, and ˜0.2n 2 empty hexagons.

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Authors: Pavel Valtr, Gábor Lippner and Gyula Károlyi


A finite set of points, in general position in the plane, is almost convex if every triple determines a triangle with at most one point in its interior. For every ℓ ≥ 3, we determine the maximum size of an almost convex set that does not contain the vertex set of an empty convex ℓ-gon.

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