Cops and robbers on oriented toroidal grids

Sebastian Gonzalez Hermosillo de la Maza, Seyyed Aliasghar Hosseini, Fiachra Knox, Bojan Mohar, Bruce Reed

Published 2019-04-23Version 1

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.