Vsevolod Voronov

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20242026

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math.MG2026

A counterexample to Gale's conjecture in $R^{3}$

Vsevolod Voronov

It is known that for every partition of the sphere $S^{2}$ of unit diameter into four parts, the largest diameter of a part is at least $(3 + 3) /6 = 0.88807 \dots$ , and th…

math.CO2026

Ordinary and measurable colorings of Euclidean three-space

Mikhail Koshelev, Andrey Kupavskii, Vsevolod Voronov

A proper coloring of Euclidean space is a coloring that assigns different colors to points at distance one. Using the planar character-law rigidity theorem of OpenAI, we prove that…

math.CO2026

The chromatic number of Euclidean space with dense color classes

Maxim Didin, Vsevolod Voronov

In this note we construct colorings of Euclidean space $R^{n}$ with finitely many colors such that any two points at unit distance have different colors and, in addition, ea…

math.MG2026

Reducing the upper bound for the Borsuk number in $R^{4}$ to 8

Alexander Tolmachev, Vsevolod Voronov

The Borsuk number $b (n)$ of $n$ -dimensional Euclidean space $R^{n}$ is the smallest integer such that any set $F \subset R^{n}$ of unit diameter can be partitioned in…

A counterexample to Gale's conjecture in R3

Ordinary and measurable colorings of Euclidean three-space

The chromatic number of Euclidean space with dense color classes

Reducing the upper bound for the Borsuk number in R4 to 8

A counterexample to Gale's conjecture in $R^{3}$

Reducing the upper bound for the Borsuk number in $R^{4}$ to 8