The Pursuit-Evasion Game on the 1-Skeleton Graph of a Regular Polyhedron. II
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 Institute of Architecture and Civil Engineering, Tashkent, Uzbekistan
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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 M of regular polyhedrons of three types in the spaces ℝd, d ≥ 3. Like in Part I, the goal is to find an integer N(M) with the following property: if n ≥ N(M), then the group of pursuers wins the game; if n < N(M), the evader wins. It is shown that N(M) = 2 for the d-dimensional simplex or cocube (a multidimensional analog of octahedron) and N(M) = [d/2] + 1 for the d-dimensional cube.
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