The CC-Game: A Variant Of The Game Of Cops And Robbers

Cops and Robbers is a vertex pursuit game played on graphs. The objective of the game, as the name suggests, is for a set of cops to catch the robber. We study a new variant of this game in which the robber can attack a cop or fight back. This variation restricts the movement of the cops and changes many of the parameters and strategies achieved in the regular game. We explore aspects of this variant such as classifications for certain cop numbers, upper and lower bounds, strategies on special graphs, the cop number on products of graphs, complexity of computations, and density of cops in infinite graphs.