# 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}
}
• Published 21 May 2020
• Mathematics
• Journal of Graph Theory

### Meyniel Extremal Families of Abelian Cayley Graphs

• Mathematics
Graphs and Combinatorics
• 2022
We study the game of Cops and Robbers, where cops try to capture a robber on the vertices of a graph. Meyniel’s conjecture states that for every connected graph G on n vertices, the cop number of G

### Cops and robbers in a random graph

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• 2013

### On Meyniel's conjecture of the cop number

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J. Graph Theory
• 2012
This article proves Meyniel's conjecture in special cases that G has diameter 2 or G is a bipartite graph of diameter 3, improving the best previously known upper-bound O(n/ lnn) due to Chiniforooshan.

### A Bound for the Cops and Robbers Problem

• Mathematics
SIAM J. Discret. Math.
• 2011
Improving several previous results, it is proved that the cop number of an n-vertex graph is at most n2 −ð1 þoð1ÞÞ ffiffiffiffIFFiffiffiffsiffiffi log n p .