Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revolutionaries and spies on random graphs   Pursuit-evasion games, such as the game of Revolutionaries and Spies, are a
simplified model for network security. In the game we consider in this paper, a
team of $r$ revolutionaries tries to hold an unguarded meeting consisting of
$m$ revolutionaries. A team of $s$ spies wants to prevent this forever. For
given $r$ and $m$, the minimum number of spies required to win on a graph $G$
is the spy number $\sigma(G,r,m)$. We present asymptotic results for the game
played on random graphs $G(n,p)$ for a large range of $p = p(n), r=r(n)$, and
$m=m(n)$. The behaviour of the spy number is analyzed completely for dense
graphs (that is, graphs with average degree at least $n^{1/2+\eps}$ for some
$\eps > 0$). For sparser graphs, some bounds are provided.

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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci