Geodesic
Chromatic numbers of real and rational spaces with real or rational forbidden distances
Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 579-612

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Several important aspects of the Nelson-Erdős-Hadwiger classical problem of combinatorial geometry are considered. In particular, new lower bounds are obtained for the chromatic numbers of the spaces $\mathbb{R}^n$ and $\mathbb{Q}^n$ with two, three or four forbidden distances. Bibliography: 28 titles. 
@article{SM_2008_199_4_a5,
     author = {A. M. Raigorodskii and I. M. Shitova},
     title = {Chromatic numbers of real and rational spaces with real or rational forbidden distances},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {199},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_4_a5/}
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A. M. Raigorodskii; I. M. Shitova. Chromatic numbers of real and rational spaces with real or rational forbidden distances. Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 579-612. http://geodesic.mathdoc.fr/item/SM_2008_199_4_a5/