Geodesic
The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron.~II
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 8 (2016) no. 4, pp. 3-13.

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Part II of the paper considers a game between a group of $n$ pursuers and one evader that move along the $1$-Skeleton graph $\mathbf{M}$ of regular polyhedrons of three types in the spaces $\mathbb{R}^d$, $d\geqslant 3$. Like in Part I, the goal is to find an integer $N(\mathbf{M})$ with the following property: if $n\geqslant N(\mathbf{M})$, then the group of pursuers wins the game; if $n$, the evader wins. It is shown that $N(\mathbf{M})=2$ for the $d$-dimensional simplex or cocube (a multidimensional analog of octahedron) and $N(\mathbf{M})=[d/2]+1$ for the $d$-dimensional cube.
Keywords: pursuit-evasion game, approach problem, evasion problem, positional strategy, counterstrategy, exact capture, regular polyhedron, one-dimensional skeleton, graph. 
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     title = {The pursuit-evasion game on the 1-skeleton graph of a regular {polyhedron.~II}},
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Abdulla A. Azamov; Atamurat Sh. Kuchkarov; Azamat G. Holboyev. The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron.~II. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 8 (2016) no. 4, pp. 3-13. http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a0/

[1] Azamov A. A., Kuchkarov A. Sh., Xolboev A. G., “Igra presledovaniya-ubeganiya na rebernom ostove pravilnykh mnogogrannikov. I”, Matematicheskaya Teoriya Igr i ee Prilozheniya, 7:3 (2015), 3–15

[2] Berzhe M., Geometriya, v. 1, Mir, M., 1984