Vsevolod Voronov

activity

20242026

collaborators

8 papers

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…

math.CO2025

On forest and bipartite cuts in sparse graphs

Ilya I. Bogdanov, Elizaveta Neustroeva, Georgy Sokolov +3

The paper is devoted to sufficient conditions for the existence of vertex cuts in simple graphs, where the induced subgraph on the cut vertices belongs to a specified graph class.…

math.CO2025

The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube

Igor Batmanov, Vsevolod Voronov

In the papers Ziegler(2001) and Goldstein(2012) it was previously shown that any subset of the Boolean cube $S \subset {0, 1}^{n}$ for $n \leq 9$ can be partitioned into $n + 1$ p…

math.CO2025

On the chromatic number of the plane for map-type colorings

Georgy Sokolov, Vsevolod Voronov

We consider the Hadwiger-Nelson problem on the chromatic number of the plane under conditions of coloring a map containing a finite number of vertices in any bounded region. Woodal…

math.MG2024

Optimal partitions of the flat torus into parts of smaller diameter

Dmitry Protasov, Alexander Tolmachev, Vsevolod Voronov

We consider the problem of partitioning a two-dimensional flat torus $T^{2}$ into $m$ sets in order to minimize the maximal diameter of a part. For $m ⩽ 25$ we give numerical…

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

On forest and bipartite cuts in sparse graphs

The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube

On the chromatic number of the plane for map-type colorings

Optimal partitions of the flat torus into parts of smaller diameter

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

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