Empty Convex Hexagons in Planar Point Sets
نویسنده
چکیده
Erdős asked whether every sufficiently large set of points in general position in the plane contains six points that form a convex hexagon without any points from the set in its interior. Such a configuration is called an empty convex hexagon. In this paper, we answer the question in the affirmative. We show that every set that contains the vertex set of a convex 9-gon also contains an empty convex hexagon.
منابع مشابه
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.
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 39 شماره
صفحات -
تاریخ انتشار 2008