All finite sets are Ramsey in the maximum norm

被引：8

作者：

Kupavskii, Andrey ^{[1
,2
,3
]}

Sagdeev, Arsenii ^{[4
]}

机构：

[1] MIPT, Moscow, Russia

[2] IAS, Princeton, NJ USA

[3] CNRS, Grenoble, France

[4] MIPT, Moscow, Russia

来源：

FORUM OF MATHEMATICS SIGMA | 2021年 / 9卷

基金：

俄罗斯基础研究基金会;

关键词：

CHROMATIC-NUMBERS; SPACES; BOUNDS;

D O I：

10.1017/fms.2021.50

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For two metric spaces X and Y the chromatic number x(X; Y) of X with forbidden Y is the smallest k such that there is a colouring of the points of X with k colors that contains no monochromatic copy of Y. In this article, we show that for each finite metric space M that contains at least two points the value chi (R-infinity(n); M) grows exponentially with n. We also provide explicit lower and upper bounds for some special M.

引用

页数：12

共 33 条

[1]

[Anonymous], 2013, Thirty Essays on Geometric Graph Theory, DOI [10.1007/978-1-4614-0110-0_23, DOI 10.1007/978-1-4614-0110-0_23]

[2] A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics l1 and l2 [J].