# 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…

## 5 Citations

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It is proved that there are arbitrarily large subcubic graphs $G$ whose cop number is at least $n^{1/2-o(1)}$ where $n=|V(G)$ and it is shown that proving Meyniel's conjecture for graphs of bounded degree implies a weak Meynels' conjecture for all graphs.

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It is proved that the cop number of all claw-free even-hole-free graphs is at most two and, in addition, the capture time is at least 2n rounds, where n is the number of vertices of the graph.

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Cops and Robbers is a classical pursuit and evasion game in graph theory, which was introduced by Nowakowski and Winkler and independently by Quilliot. In this paper, we study the zero-visibility…

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We consider the game of cops and robbers, which is a game played on a finite graph G by two players, Alice and Bob. Alice controls a team of cops, and Bob controls a robber, both of which occupy…

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