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The game of Cops and Robber is a pursuit-evasion game which is usually playedon a connected graph. In the game, a set of cops and a robber move around thevertices of a graph along edges, where the cops aim to capture the robber,while the robber aims to avoid capture. Much research about this game have beendone since the early 1980s. The game has a natural generalisation to beingplayed on connected hypergraphs, where the cops and the robber may now movealong hyperedges. In this paper, we shall provide a characterisation of allhypergraphs where one cop is sufficient to capture the robber. The cop-numberof a connected hypergraph is the minimum number of cops required in order tocapture the robber. We shall prove some results about the cop-number of certainhypergraphs, including hypertrees and Cartesian products of hypergraphs.

Cops and Robber on Cartesian products and some classes of hypergraphs