A note on coloring line arrangements

被引：0

作者：

Ackerman, Eyal ^{[1
]}

Pach, Janos ^{[2
,3
]}

Pinchasi, Rom ^{[4
]}

Radoicic, Rados ^{[5
]}

Toth, Geza ^{[3
]}

机构：

[1] Univ Haifa, Dept Math Phys & Comp Sci, IL-36006 Tivon, Israel

[2] Ecole Polytech Fed Lausanne, CH-1015 Lausanne, Switzerland

[3] Alfred Renyi Inst, Budapest, Hungary

[4] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[5] CUNY, Baruch Coll, Dept Math, New York, NY 10021 USA

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2014年 / 21卷 / 02期

基金：

瑞士国家科学基金会;

关键词：

Arrangements of lines; chromatic number; sparse hypergraphs; SETS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the lines of every arrangement of n lines in the plane can be colored with O(root n/log n) colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a circle minus(root/log n) factor. Any further improvement on this bound would also improve the best known lower bound on the following problem of Erdos: estimate the maximum number of points in general position within a set of n points containing no four collinear points.

引用

页数：4