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On the chromatic numbers of small-dimensional Euclidean spaces

Discrete Applied Mathematics. 2018. Vol. 243. P. 125-131.
Cherkashin Danila, Kulikov A., Andrei Raigorodskii.

This paper is devoted to the study of the graph sequence Gn = (Vn, En), where Vn is the set of all vectors v ∈ R n with coordinates in {−1, 0, 1} such that |v| = √ 3 and En consists of all pairs of vertices with scalar product 1. We find the exact value of the independence number of Gn. As a corollary we get new lower bounds on χ(R n ) and χ(Qn ) for small values of n.