@article {IOPORT.06045747,
    author       = {Frieze, Alan and Krivelevich, Michael and Loh, Po-Shen},
    title        = {Variations on cops and robbers.},
    year         = {2012},
    journal      = {Journal of Graph Theory},
    volume       = {69},
    number       = {3-4},
    issn         = {0364-9024},
    pages        = {383-402},
    publisher    = {John Wiley \& Sons, New York, NY},
    doi          = {10.1002/jgt.20591},
    abstract     = {Summary: We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move $R\ge 1$ edges at a time, establishing a general upper bound of $n/\alpha^{(1-0(1))}\sqrt {\log_{\alpha}n}$, where $\alpha = 1 + 1/R$, thus generalizing the best known upper bound for the classical case $R = 1$ due to {\it L. Lu} and {\it X. Peng} [``On Meyniel conjecture of the cop number" (submitted)], and {\it A. Scott} and {\it B. Sudakov} [``A new bound for the cops and robbers problem", \url{arXiv:1004.2010}]. We also show that in this case, the cop number of an $n$-vertex graph can be as large as $n^{1 - 1/(R - 2)}$ for finite $R\ge 5$, but linear in $n$ if $R$ is infinite. For $R = 1$, we study the directed graph version of the problem, and show that the cop number of any strongly connected digraph on n vertices is $O(n(\log\log n)^{2}/\log n)$. Our approach is based on expansion.},
    identifier   = {06045747},
}