On the chromatic numbers of small-dimensional Euclidean spaces
Combinatorics
2016-08-31 v2 Metric Geometry
Abstract
The paper is devoted to the study of graph sequence G_n = (V_n, E_n) where V_n is the set of all vectors v in R^n with coordinates from {-1, 0, 1} such that |v| = sqrt(3), and E_n consists of all pairs of vertices with the scalar product 1. We find exactly the independence number of G_n. As a corollary we get some new lower bounds of chi(\R^n) and chi(\Q^n) for small values of n.
Keywords
Cite
@article{arxiv.1512.03472,
title = {On the chromatic numbers of small-dimensional Euclidean spaces},
author = {Danila Cherkashin and Anatoly Kulikov and Andrey Raigorodskii},
journal= {arXiv preprint arXiv:1512.03472},
year = {2016}
}
Comments
12 pages