On the number of points in general position in the plane

被引：13

作者：

Balogh, Jozsef ^{[1
]}

Solymosi, Jozsef ^{[2
]}

机构：

[1] Univ Illinois, Dept Math Sci, Urbana, IL 61801 USA

[2] Univ British Columbia, Dept Math, 1984 Math Rd, Vancouver, BC V6T 1Z4, Canada

来源：

DISCRETE ANALYSIS | 2018年

基金：

加拿大自然科学与工程研究理事会;

关键词：

General point sets in the plane; epsilon-nets; Hypergraph container method; DENSITY VERSION; EPSILON-NETS; SYSTEMS; BOUNDS; SIZE;

D O I：

10.19086/da.4438

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study some Erdos type problems in discrete geometry. Our main result is that we show that there is a planar point set of n points such that no four are collinear but no matter how we choose a subset of size n(5/6 +o(1)) it contains a collinear triple. Another application studies epsilon-nets in a point-line system in the plane. We prove the existence of some geometric constructions with a new tool, the so-called Hypergraph Container Method.

引用

页数：20

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