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.
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页数：20
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