5 papers · 1 filter
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…
The chromatic number of Euclidean space with dense color classes
Maxim Didin, Vsevolod Voronov
In this note we construct colorings of Euclidean space with finitely many colors such that any two points at unit distance have different colors and, in addition, ea…
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.…
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 for can be partitioned into p…
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…