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math.CO2010★ 6 cited
On the chromatic numbers of spheres in
Andrei Raigorodskii
In this paper, we obtain new asymptotic lower bounds for the chromatic numbers of spheres.
math.CO2010★ 5 cited
Counterexamples to Borsuk's conjecture on spheres of small radii
Andrei Kupavskii, Andrei Raigorodskii
In this work, the classical Borsuk conjecture is discussed, which states that any set of diameter 1 in the Euclidean space can be divided into parts of sm…