English

Cops and robbers on oriented toroidal grids

Combinatorics 2020-05-13 v2 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.1904.10113,
  title  = {Cops and robbers on oriented toroidal grids},
  author = {Sebastian Gonzalez Hermosillo de la Maza and Seyyed Aliasghar Hosseini and Fiachra Knox and Bojan Mohar and Bruce Reed},
  journal= {arXiv preprint arXiv:1904.10113},
  year   = {2020}
}
R2 v1 2026-06-23T08:46:51.037Z