Cops, Robber, and Alarms

The two games considered are mixtures of Searching and Cops and Robber. The cops have partial information, provided first via selected vertices of a graph, and then via selected edges. This partial information includes the robber's position, but not the direction in which he is moving. The robber has perfect information. In both cases, we give bounds on the amount of such information required by a single cop to guarantee the capture of the robber on a copwin graph.