ABSTRACT
The game of Cops and Robbers is lucky to possess many beautiful and natural variations. This chapter focuses on those variations where the settings of the probabilistic method have been applied. It considers a variant of Cops and Robbers played on edges, and provides bounds on the cop number where the robber is allowed to move with unbounded speed. In this variant, the rules are identical as before, except for the movement of the robber: on the robber's turn, they may move to any vertex connected to their present position, so long as the path does not go through a vertex occupied by a cop. The chapter considers Lazy Cops and Robbers, where only one cop may move in a given round. It then considers a variant of the game on a hypercube that restricts the initial positions and the allowed moves. This variant restricts the initial positions and the allowed moves. The chapter discusses another variant, the containment game.
