On the chromatic numbers of small-dimensional Euclidean spaces
Abstract
The paper is devoted to the study of graph sequence Gn = (Vn, En) where Vn is the set of all vectors v in Rn with coordinates from -1, 0, 1 such that |v| = sqrt(3), and En consists of all pairs of vertices with the scalar product 1. We find exactly the independence number of Gn. As a corollary we get some new lower bounds of chi(n) and chi(n) for small values of n.
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