Empty convex hexagons in planar point sets

被引：61

作者：

Gerken, Tobias ^{[1
]}

机构：

[1] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2008年 / 39卷 / 1-3期

关键词：

Erdos-Szekeres problem; Ramsey theory; convex polygons and polyhedra; empty hexagon problem;

D O I：

10.1007/s00454-007-9018-x

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Erdos 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.

引用

页码：239 / 272

页数：34

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