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Cops and Robber game in higher-dimensional manifolds with spherical and Euclidean metric

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arxiv 2211.02290 v1 pith:RDKET5W4 submitted 2022-11-04 math.MG

classification math.MG
keywords gamecopsrobberstrategiesstrategyappliedballcovering
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abstract

The recently introduced variation of the game of cops and robber is played on geodesic spaces. In this paper we establish some general strategies for the players, in particular the generalized radial strategy and the covering space strategy. Those strategies are then applied to the game on the $n$-dimensional ball, the sphere, and the torus.

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