%0 Journal Article %T Size of components of a cube coloring %A Marsel Matdinov %J Mathematics %D 2011 %I arXiv %X Suppose a d-dimensional lattice cube of size n^d is colored in several colors so that no face of its triangulation (subdivision of the standard partition into n^d small cubes) is colored in m+2 colors. Then one color is used at least f(d,m)*n^(d-m) times. %U http://arxiv.org/abs/1111.3911v1