Vesna Iršič, Faculty of Mathematics and Physics, University of Ljubljana and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia; e-mail: vesna.irsic@fmf.uni-lj.si

Bojan Mohar, FRSC, Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada; e-mail: mohar@sfu.ca

Alexandra Wesolek, Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada; e-mail: agwesole@sfu.ca

Abstract/Résumé:

A 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.

Le jeu aux gendarmes et aux voleurs sur les espaces géodésiques est analysé. On établit quelques stratégies générales pour les joueurs, en particulier la stratégie radiale généralisée et la stratégie d’espaces de couverture universels. Ces stratégies sont ensuite appliquées aux jeux sur la boule de dimension \(n\), sur la sphère, et sur le tore.

Keywords: Game of cops and robber, geodesic space, radial strategy

AMS Subject Classification: Metric spaces; metrizability, Differential games, Discrete-time games 54E35, 91A23, 91A50

PDF(click to download): Cops and Robber Game in Higher-dimensional Manifolds with Spherical and Euclidean Metric