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Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2019, Volume 11, Issue 4, Pages 5–23
(Mi mgta246)
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This article is cited in 3 scientific papers (total in 3 papers)
The pursuit-evasion game on the $1$-skeleton graph of the regular polyhedron. III
Abdulla A. Azamov, Atamurat Sh. Kuchkarov, Azamat G. Holboyev Institute of Mathematics
Abstract:
It is considered a game between a group of $n$ pursuers and one evader moving with the same maximal speed along $1$-skeleton of a given regular polyhedron. In this paper it is considered the case of the regular polyhedrons with $24$ and $120$ vertices in the space $\mathbb{R}^4$. It is proven that if $n \leqslant 2$, then the evader wins in the game, and to the evader, if $n \geqslant 3$ then the game finishes successfully for the group of pursuers.
Keywords:
pursuit-evasion game, approach problem, evasion problem, positional strategy, counter strategy, exact catch, regular polyhedron with $24$ vertices, regular polyhedron with $120$ vertices, one-dimensional graph.
Received: 16.01.2019 Revised: 25.04.2019 Accepted: 10.06.2019
Citation:
Abdulla A. Azamov, Atamurat Sh. Kuchkarov, Azamat G. Holboyev, “The pursuit-evasion game on the $1$-skeleton graph of the regular polyhedron. III”, Mat. Teor. Igr Pril., 11:4 (2019), 5–23
Linking options:
https://www.mathnet.ru/eng/mgta246 https://www.mathnet.ru/eng/mgta/v11/i4/p5
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