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

共 50 条

[21] The conformal representation of the various triangles bounded by the arcs of three intersecting circles
Hodgkinson, J
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1916, 15 : 166 - 181
[22] Thresholds for intersecting D-branes revisited
Akerblom, Nikolas
Blumenhagen, Ralph
Luest, Dieter
Schmidt-Sommerfeld, Maximilian
[J]. PHYSICS LETTERS B, 2007, 652 (01) : 53 - 59
[23] An Improved Bound on the Number of Unit Area Triangles
Apfelbaum, Roel
Sharir, Micha
[J]. PROCEEDINGS OF THE TWENTY-FIFTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SCG'09), 2009, : 135 - 140
[24] A lazy version of Eppstein's K shortest paths algorithm
Jiménez, VM
Marzal, A
[J]. EXPERIMENTAL AND EFFICIENT ALGORITHMS, PROCEEDINGS, 2003, 2647 : 179 - 190
[25] An Improved Bound on the Number of Unit Area Triangles
Apfelbaum, Roel
Sharir, Micha
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2010, 44 (04) : 753 - 761
[26] An Improved Bound on the Number of Unit Area Triangles
Roel Apfelbaum
Micha Sharir
[J]. Discrete & Computational Geometry, 2010, 44 : 753 - 761
[27] String junctions and bound states of intersecting branes
Berenstein, D
Leigh, RG
[J]. PHYSICAL REVIEW D, 1999, 60 (02)
[28] Acyclic Edge Coloring Conjecture Is True on Planar Graphs Without Intersecting Triangles
Shu, Qiaojun
Chen, Yong
Han, Shuguang
Lin, Guohui
Miyano, Eiji
Zhang, An
[J]. THEORY AND APPLICATIONS OF MODELS OF COMPUTATION, TAMC 2020, 2020, 12337 : 426 - 438
[29] Acyclic edge coloring conjecture is true on planar graphs without intersecting triangles
Shu, Qiaojun
Chen, Yong
Han, Shuguang
Lin, Guohui
Miyano, Eiji
Zhang, An
[J]. THEORETICAL COMPUTER SCIENCE, 2021, 882 : 77 - 108
[30] Intersecting M-branes and bound states
Khviengia, N
Khviengia, Z
Lu, H
Pope, CN
[J]. PHYSICS LETTERS B, 1996, 388 (01) : 21 - 28

← 1 2 3 4 5 →