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Coloring Some Finite Sets in ℝn

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Balogh J., Kostochka A., Raigorodskii A.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 1

25-31

This note relates to bounds on the chromatic number χ(ℝn) of the Euclidean space, which is the minimum number of colors needed to color all the points in ℝn so that any two points at the distance 1 receive different colors. In [6] a sequence of graphs Gn in ℝn was introduced showing that . For many years, this bound has been remaining the best known bound for the chromatic numbers of some lowdimensional spaces. Here we prove that and find an exact formula for the chromatic number in the case of n = 2k and n = 2k − 1.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Balogh J.

1 Kostochka A.

1 Raigorodskii A.

1 2013

Wyniki wyszukiwania

Coloring Some Finite Sets in ℝn