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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Mehrabian, Abbas 2015. The fast robber on interval and chordal graphs. Discrete Applied Mathematics, Vol. 180, p. 188.

    Fomin, Fedor V. Giroire, Frédéric Jean-Marie, Alain Mazauric, Dorian and Nisse, Nicolas 2014. To satisfy impatient Web surfers is hard. Theoretical Computer Science, Vol. 526, p. 1.

    Mi, Shichao Zhu, Shanying Chen, Cailian and Guan, Xinping 2013. TWGS:A Tree Decomposition Based Indoor Pursuit-Evasion Game For Robotic Networks. IFAC Proceedings Volumes, Vol. 46, Issue. 13, p. 135.

    Fomin, Fedor V. Golovach, Petr A. and Prałat, Paweł 2012. Cops and Robber with Constraints. SIAM Journal on Discrete Mathematics, Vol. 26, Issue. 2, p. 571.

  • Combinatorics, Probability and Computing, Volume 20, Issue 4
  • July 2011, pp. 617-621

Lower Bounds for the Cop Number when the Robber is Fast

  • DOI:
  • Published online: 19 April 2011

We consider a variant of the Cops and Robbers game where the robber can move t edges at a time, and show that in this variant, the cop number of a d-regular graph with girth larger than 2t+2 is Ω(dt). By the known upper bounds on the order of cages, this implies that the cop number of a connected n-vertex graph can be as large as Ω(n2/3) if t ≥ 2, and Ω(n4/5) if t ≥ 4. This improves the Ω() lower bound of Frieze, Krivelevich and Loh (Variations on cops and robbers, J. Graph Theory, to appear) when 2 ≤ t ≤ 6. We also conjecture a general upper bound O(nt/t+1) for the cop number in this variant, generalizing Meyniel's conjecture.

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[4]F. V. Fomin , P. A. Golovach , J. Kratochvíl , N. Nisse and K. Suchan (2010) Pursuing a fast robber on a graph. Theoret. Comput. Sci. 411 11671181.

[5]P. Frankl (1987) Cops and robbers in graphs with large girth and Cayley graphs. Discrete Appl. Math. 17 301305.

[10]R. Nowakowski and P. Winkler (1983) Vertex-to-vertex pursuit in a graph. Discrete Math. 43 235239.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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