G. Strukov

activity

20202022

collaborators

4 papers

math.CO2022

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 $ε > 0$ holds \[ χ(\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where $χ (M)$ stands for the chromatic number of an (infinite) graph w…

math.CO2022

Erd\H os--Hajnal problem for $H$ -free hypergraphs

Danila Cherkashin, Alexei Gordeev, Georgii Strukov

This paper deals with the minimum number $m_{H} (r)$ of edges in an $H$ -free graph with the chromatic number more than $r$ . We show how bounds on Ramsey and Turán numbers imply bounds…

math.MG2021

Maximal distance minimizers for a rectangle

D. D. Cherkashin, A. S. Gordeev, G. A. Strukov +1

\emph{A maximal distance minimizer} for a given compact set $M \subset R^{2}$ and some given $r > 0$ is a set having the minimal length (one-dimensional Hausdorff measure) o…

math.CO2020

On minimizers of the maximal distance functional for a planar convex closed smooth curve

D. D. Cherkashin, A. S. Gordeev, G. A. Strukov +1

Fix a compact $M \subset R^{2}$ and $r > 0$ . A minimizer of the maximal distance functional is a connected set $Σ$ of the minimal length, such that \[ max_{y \in M} dist(y,Σ)…

On the chromatic numbers of 3-dimensional slices

Erd\H os--Hajnal problem for H-free hypergraphs

Maximal distance minimizers for a rectangle

On minimizers of the maximal distance functional for a planar convex closed smooth curve

Erd\H os--Hajnal problem for $H$ -free hypergraphs