Cops and Robber on Butterflies and Solid Grids

Sheikh Shakil Akhtar, Sandip Das, Harmender Gahlawat

Abstract: Cops and robber is a well-studied two player pursuit-evasion game played on a graph. In this game, a set of cops, controlled by the first player, tries to capture the position of a robber, controlled by the second player. The cop number of a graph is the minimum number of cops required to capture the robber in the graph. We show that the cop number for butterfly networks and for solid grids is two.