Geodesic
On rational analogs of Nelson--Hadwiger's and Borsuk's problems
Čebyševskij sbornik, Tome 19 (2018) no. 3, pp. 270-281

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In this paper, we consider affine-rational analogs of Nelson–Hadwiger problem on finding the chromatic number of the rational space and Borsuk's problem on partitioning into parts of smaller diameter. New lower bounds are proved. In particular, bounds on the minimum dimension of a counterexample to Borsuk's conjecture are found.
Keywords: Chromatic number, unit-distance graphs, Borsuk's problem. 
@article{CHEB_2018_19_3_a21,
     author = {A. Sokolov and A. M. Raigorodskiy},
     title = {On rational analogs of {Nelson--Hadwiger's} and {Borsuk's} problems},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {270--281},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2018_19_3_a21/}
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A. Sokolov; A. M. Raigorodskiy. On rational analogs of Nelson--Hadwiger's and Borsuk's problems. Čebyševskij sbornik, Tome 19 (2018) no. 3, pp. 270-281. http://geodesic.mathdoc.fr/item/CHEB_2018_19_3_a21/