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

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

2011-09-06

arxiv.org/abs/1109.1078v2

Mathematics

Combinatorics

Scientific paper

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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