6 citations · 13 across the 5 of their papers we have counts for
5 papers
The chromatic number of the plane with an interval of forbidden distances is at least 7
Vsevolod Voronov
The work is devoted to one of the variations of the Hadwiger--Nelson problem on the chromatic number of the plane. In this formulation one needs to find for arbitrarily small $\var…
Coverings of planar and three-dimensional sets with subsets of smaller diameter
Alexander Tolmachev, Dmitry Protasov, Vsevolod Voronov
Quantitative estimates related to the classical Borsuk problem of splitting set in Euclidean space into subsets of smaller diameter are considered. For a given there is a minim…
On the chromatic numbers of 3-dimensional slices
D. D. Cherkashin, A. J. Kanel-Belov, G. A. Strukov +1
We prove that for an arbitrary holds \[ χ(\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where stands for the chromatic number of an (infinite) graph w…
On the chromatic number of 2-dimensional spheres
Danila Cherkashin, Vsevolod Voronov
In 1976 Simmons conjectured that every coloring of a 2-dimensional sphere of radius strictly greater than in three colors has a couple of monochromatic points at the distance…
Constructing 5-chromatic unit distance graphs embedded in the Euclidean plane and two-dimensional spheres
Vsevolod Voronov, Anna Neopryatnaya, Eugene Dergachev
This paper is devoted to the development of algorithms for finding unit distance graphs with chromatic number greater than 4, embedded in a two-dimensional sphere or plane. Such gr…