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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 for can be partitioned into 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…