“…The cops and robbers game has attracted considerable attention from the graph theory community, owing in part to its connections to various graph parameters, as well as the large number of interesting combinatorial problems arising from the study of the cop number. In addition, due to the relative simplicity and naturalness of the cops and robbers game, it has served as a model for studying problems in areas of applied computer science such as artificial intelligence, robotics and the theory of optimal search [8,11,15,21]. This paper examines a variant of the cops and robbers game, known alternately as the oneactive-cop game [17], lazy cops and robbers game [3,4,22] or the one-cop-moves game [25].…”