Improved bounds on the cop number when forbidding a minor

@article{Kenter2023ImprovedBO,
  title={Improved bounds on the cop number when forbidding a minor},
  author={Franklin Kenter and Erin Meger and J{\'e}r{\'e}mie Turcotte},
  journal={ArXiv},
  year={2023},
  volume={abs/2302.14851}
}
Andreae (1986) proved that the cop number of connected $H$-minor-free graphs is bounded for every graph $H$. In particular, the cop number is at most $|E(H-h)|$ if $H-h$ contains no isolated vertex. The main result of this paper is an improvement on this bound, which is most significant when $H$ is small or sparse, for instance when $H-h$ can be obtained from another graph by multiple edge subdivisions. Some consequences of this result are improvements on the upper bound for the cop number of… 
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23 References

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