Primal-Dual Cops and Robber
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Cops and Robber is a family of two-player games played on graphs in which one player controls a number of cops and the other player controls a robber. In alternating turns, each player moves (all) his/her figures. The cops try to capture the robber while the latter tries to flee indefinitely. In this paper we consider a variant of the game played on a planar graph where the robber moves between adjacent vertices while the cops move between adjacent faces. The cops capture the robber if they occupy all incident faces. We prove that a constant number of cops suffices to capture the robber on any planar graph of maximum degree Δ if and only if Δ≤ 4.
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