On a Generalization of Meyniel's Conjecture on the Cops and Robbers Game

@article{Alon2011OnAG,
  title={On a Generalization of Meyniel's Conjecture on the Cops and Robbers Game},
  author={Noga Alon and Abbas Mehrabian},
  journal={Electr. J. Comb.},
  year={2011},
  volume={18}
}
We consider a variant of the Cops and Robbers game where the robber can move s edges at a time, and show that in this variant, the cop number of a connected graph on n vertices can be as large as Ω(n s s+1 ). This improves the Ω(n s−3 s−2 ) lower bound of Frieze et al. [5], and extends the result of the second author [10], which establishes the above bound for s = 2, 4. 

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