Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some...