Limited-visibility Cops and Robbers on Hamming graphs

In the classic game of Cops and Robbers, a team of cops pursues a robber through a graph. The traditional model of Cops and Robbers operates under the assumption that the cops know the robber's location at all times. Recently, however, there has been growing interest in models wherein the cops have only partial information about the robber's location. In this paper, we study the limited-visibility variant of Cops and Robbers, in which the cops only know the robber's position if some cop is within a fixed distance of the robber. For this variant of the game, we give bounds on the number of cops needed to capture a robber on Hamming graphs, and we use these results to settle several open problems posed by Clarke et al.