# Surrounding cops and robbers on graphs of bounded genus

@article{Bradshaw2019SurroundingCA, title={Surrounding cops and robbers on graphs of bounded genus}, author={Peter Bradshaw and Seyyed Aliasghar Hosseini}, journal={arXiv: Combinatorics}, year={2019} }

We consider a surrounding variant of cops and robbers on graphs of bounded genus. We obtain bounds on the number of cops required to surround a robber on planar graphs, toroidal graphs, and outerplanar graphs. We also obtain improved bounds for bipartite planar and toroidal graphs. We briefly consider general graphs of bounded genus and graphs with a forbidden minor.

## 3 Citations

### C O ] 3 1 O ct 2 01 9 Cops that Surround a Robber

- Mathematics
- 2019

We introduce the game of Surrounding Cops and Robber on a graph, as a variant of the traditional game of Cops and Robber. In contrast to the traditional game in which the cops win by occupying the…

### Simultaneous Moves with Cops and an Insightful Robber

- Computer ScienceArXiv
- 2020

In graphs where retracts are involved, it is shown how cop strategies against a robber can be modified to capture a robot, which gives exact numbers for hypercubes, and $k$-dimensional grids in general.

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