Eppstein's bound on intersecting triangles revisited

被引：8

作者：

Nivasch, Gabriel ^{[1
]}

Sharir, Micha ^{[1
]}

机构：

[1] Tel Aviv Univ, Sch Comp Sci, IL-69978 Tel Aviv, Israel

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2009年 / 116卷 / 02期

基金：

美国国家科学基金会;

关键词：

Triangle; Simplex; Selection Lemma; k-set; HALVING PLANES;

D O I：

10.1016/j.jcta.2008.07.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a set of it points in the plane, and let T be a set of in triangles with vertices in S. Then there exists a point in the plane contained in Omega(m(3)/(n(6)log(2)n)) triangles of T. Eppstein [D, Eppstein, Improved bounds for intersecting triangles and halving planes, J. Combin. Theory Ser. A 62 (1993) 176-182] gave a proof of this claim, but there is a problem with his proof. Here we provide a correct proof by slightly modifying Eppstein's argument. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：494 / 497

页数：4

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