Fully Active Cops and Robbers

Abstract: We study a variation of the classical pursuit-evasion game of Cops and Robbers in which agents are required to move to an adjacent vertex on every turn. We explore how the minimum number of cops needed to catch the robber can change when this condition is added to the rules of the game. We study this `Fully Active Cops and Robbers' game for a number of classes of graphs and present some open problems for future research.