The Pursuit-Evasion Game on the 1-Skeleton Graph of a Regular Polyhedron. II

Abstract

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 ℝ^d, 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.