A robber locating strategy for trees

The robber locating game, introduced by Seager (2012), is a variation of the classic cops and robbers game on a graph. A cop attempts to locate an invisible robber on a graph by probing a single vertex v each turn, from which the cop learns the robber's distance. The robber is then permitted to stay at his current vertex or move to an adjacent vertex other than v. A graph is locatable if the cop is able to locate the robber in a finite number of probes, and the location number of a graph is the minimum number of probes necessary to determine the robber's location regardless of the robber's evasion strategy. We provide a strategy that locates the robber on trees. The number of probes used under this strategy meets, and often improves, the theoretical bound on the location number of trees.