Revolutionaries and spies on random graphs
Résumé
Pursuit-evasion games, such as the game of Revolutionaries and Spies, are a simplifi ed 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+\epsilon} for some \epsilon > 0). For sparser graphs, some bounds are provided.
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