The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. I
Абдулла АзамовInstitute of Mathematics of the National University of Uzbekistan, Tashkent, UzbekistanA. Sh. KuchkarovInstitute of Mathematics of the National University of Uzbekistan, Tashkent, UzbekistanA. G. HolboyevTashkent State Pedagogical University, Tashkent, Uzbekistan
ABI
Аннотация
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 ℝ d , d ≥ 5; and Part III, to the case of ℝ4.
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