Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variations on Cops and Robbers   We consider several variants of the classical Cops and Robbers game. We treat
the version where the robber can move R > 1 edges at a time, establishing a
general upper bound of N / \alpha ^{(1-o(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 Lu and Peng. 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, 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 at most O(N(log log N)^2/log N). Our approach is based on
expansion.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga