Cops and robbers on oriented toroidal grids

Published 23 Apr 2019 in math.CO and cs.DM | (1904.10113v2)

Abstract: The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Klein bottle and we prove that their cop number is bounded by a constant. We also show that the cop number of every k-regularly oriented toroidal grid is at most 13.

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