An Analogue of Gromov's Waist Theorem for Coloring the Cube

被引：4

作者：

Karasev, R. N. ^{[1
,2
,3
]}

机构：

[1] Moscow Inst Phys & Technol, Dept Math, Dolgoprudnyi 141700, Russia

[2] RAS, Inst Informat Transmiss Problems, Moscow 127994, Russia

[3] Yaroslavl State Univ, Lab Discrete & Computat Geometry, Yaroslavl 150000, Russia

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2013年 / 49卷 / 03期

关键词：

Graph coloring; Covering dimension; Waist inequality; POINT THEOREM;

D O I：

10.1007/s00454-013-9490-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

It is proved that if we partition a d-dimensional cube into small cubes and color the small cubes in colors then there exists a monochromatic connected component consisting of at least small cubes. Another proof of this result is given in Matdinov's preprint (Size of components of a cube coloring, arXiv:1111.3911, 2011).

引用

页码：444 / 453

页数：10

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