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

作者：Karasev R N^*

来源：Discrete & Computational Geometry, 2013, 49(3): 444-453.

DOI：10.1007/s00454-013-9490-4

• Graph coloring
• Covering dimension
• Waist inequality

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).

• 出版日期2013-4