On the cop number of graphs of high girth

@article{Bradshaw2022OnTC,
  title={On the cop number of graphs of high girth},
  author={Peter Bradshaw and Seyyed Aliasghar Hosseini and Bojan Mohar and Ladislav Stacho},
  journal={Journal of Graph Theory},
  year={2022},
  volume={102},
  pages={15 - 34}
}
We establish a lower bound for the cop number of graphs of high girth in terms of the minimum degree, and more generally, in terms of a certain growth condition. We show, in particular, that the cop number of any graph with girth g $g$ and minimum degree δ $\delta $ is at least 1 g ( δ − 1 ) ⌊ g − 1 4 ⌋ $\frac{1}{g}{(\delta -1)}^{\lfloor \frac{g-1}{4}\rfloor }$ . We establish similar results for directed graphs. While exposing several reasons for conjecturing that the exponent 1 4 g $\frac{1}{4… 

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