Computing strategies for multiple cops on infinite graphs

Cops and robbers is a vertex pursuit game played on connected reflexive graphs. While the game is most often played with a single cop on a finite graph, we consider the variation in which n cops pursue the robber on an infinite graph. For each n ⩾ 2 , we show there is a computable graph which is classically cop-win and can be won by n cops using a computable strategy, but cannot be won by n − 1 cops using a computable strategy. Furthermore, we show that the index set of n -cop-win computable graphs is Π 1 1 -complete.