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pro vyhledávání: '"Voronov, Vsevolod A."'
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 $m \leqslant 25$ we give numerical estimates for the maximal diameter $d_m(T^2)$ at which the partition
Externí odkaz:
http://arxiv.org/abs/2402.03997
Autor:
Voronov, Vsevolod
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 $\varepsilon$ the least possible number of colors needed to color a Euclide
Externí odkaz:
http://arxiv.org/abs/2304.10163
Publikováno v:
Discrete Applied Mathematics, 320, 270-281 (2022)
Quantitative estimates related to the classical Borsuk problem of splitting set in Euclidean space into subsets of smaller diameter are considered. For a given $k$ there is a minimal diameter of subsets at which there exists a covering with $k$ subse
Externí odkaz:
http://arxiv.org/abs/2210.12394
Autor:
Cherkashin, Danila, Voronov, Vsevolod
In 1976 Simmons conjectured that every coloring of a 2-dimensional sphere of radius strictly greater than $1/2$ in three colors has a couple of monochromatic points at the distance 1 apart. We prove this conjecture.
Comment: 8p
Comment: 8p
Externí odkaz:
http://arxiv.org/abs/2203.08666
Publikováno v:
Discrete Mathematics, 345(12), 113106 (2022)
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 graphs provide a lower bound for the Nelson-Hadwiger problem on the chro
Externí odkaz:
http://arxiv.org/abs/2106.11824
Autor:
Simonenko, Elizaveta P., Mokrushin, Artem S., Simonenko, Nikolay P., Voronov, Vsevolod A., Kim, Vitalii P., Tkachev, Sergey V., Gubin, Sergey P., Sevastyanov, Vladimir G., Kuznetsov, Nikolay T.
Publikováno v:
In Thin Solid Films 31 January 2019 670:46-53
Publikováno v:
In IFAC PapersOnLine 2018 51(32):704-707
Autor:
Cherkashin, Danila, Voronov, Vsevolod
Publikováno v:
Discrete & Computational Geometry; Mar2024, Vol. 71 Issue 2, p467-479, 13p
Akademický článek
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Autor:
Voronov, Vsevolod
The work is devoted to 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 $\varepsilon$ the least possible number of colors needed to color the Eu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::27a901ac13a08f53c2205f671126d9fd