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arXiv · 1109.1078

An analogue of Gromov's waist theorem for coloring the cube

Roman Karasev
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Abstract

It is proved that if we partition a $d$-dimensional cube into $n^d$ small cubes and color the small cubes into $m+1$ colors then there exists a monochromatic connected component consisting of at least $f(d, m) n^{d-m}$ small cubes.

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Roman Karasev. 2011-11-17. An analogue of Gromov's waist theorem for coloring the cube. https://doi.org/10.1007/s00454-013-9490-4

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