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We consider the well-studied cops and robbers game in the context of orientedgraphs, which has received surprisingly little attention to date. We examinethe relationship between the cop numbers of an oriented graph and itsunderlying undirected graph, giving a surprising result that there exists atleast one graph $G$ for which every strongly connected orientation of $G$ hascop number strictly less than that of $G$. We also refute a conjecture on thestructure of cop-win digraphs, study orientations of outerplanar graphs, andstudy the cop number of line digraphs. Finally, we consider some the aspects ofoptimal play, in particular the capture time of cop-win digraphs and propertiesof the relative positions of the cop(s) and robber.

A study of cops and robbers in oriented graphs