Even flying cops should think ahead

@article{Martinsson2018EvenFC,
  title={Even flying cops should think ahead},
  author={A. Martinsson and Florian Meier and P. Schnider and A. Steger},
  journal={ArXiv},
  year={2018},
  volume={abs/1801.07193}
}
We study the entanglement game, which is a version of cops and robbers, on sparse graphs. While the minimum degree of a graph G is a lower bound for the number of cops needed to catch a robber in G, we show that the required number of cops can be much larger, even for graphs with small maximum degree. In particular, we show that there are 3-regular graphs where a linear number of cops are needed. 

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