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JOURNALS // Matematicheskaya Teoriya Igr i Ee Prilozheniya // Archive

Mat. Teor. Igr Pril., 2019 Volume 11, Issue 4, Pages 5–23 (Mi mgta246)

This article is cited 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.

UDC: 517.97
BBK: 22.18

Received: 16.01.2019
Revised: 25.04.2019
Accepted: 10.06.2019



© Steklov Math. Inst. of RAS, 2025