Cops & Robber on Periodic Temporal Graphs: Characterization and Improved Bounds.

We study the classical Cops and Robber game when the cops and the robber move on an infinite periodic sequence of graphs on the same set V of n vertices: in round t , the topology of is where . As in the traditional case of static graphs , the main concern is on the characterization of the class of periodic temporal graphs where k cops can capture the robber. Concentrating on the case of a single cop, we provide a characterization of copwin periodic temporal graphs. Based on this characterization, we design an algorithm for determining if a periodic temporal graph is copwin with time complexity , where , improving the existing bound. Let us stress that, when (i.e., in the static case), the complexity becomes , improving the best existing bound.