Cops and robbers on oriented toroidal grids

2019/04/23 by Sebastian Gonzalez Hermosillo de la Maza, Seyyed Aliasghar Hosseini, de la Maza, Sebastian Gonzalez Hermosillo +7
Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO

paper · pdf · doi:10.48550/arxiv.1904.10113

arxiv created 2020/05/12 · arxiv updated 2020/05/13

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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