Abstract
We consider a game between a group of n pursuers and one evader moving with the same maximum velocity along the 1-skeleton graph of a regular polyhedron. The goal of the paper is finding, for each regular polyhedron M, a number N(M) with the following properties: if n ≥ N(M), the group of pursuers wins, while if n < N(M), the evader wins. Part I of the paper is devoted to the case of polyhedra in ℝ3; Part II will be devoted to the case of ℝd, d ≥ 5; and Part III, to the case of ℝ4.
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Original Russian Text © A.A. Azamov, A.Sh. Kuchkarov, A.G. Holboyev, 2015, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2015, No. 3, pp. 3–15.
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Azamov, A.A., Kuchkarov, A.S. & Holboyev, A.G. The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. I. Autom Remote Control 78, 754–761 (2017). https://doi.org/10.1134/S0005117917040166
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DOI: https://doi.org/10.1134/S0005117917040166