Revolutionaries and spies on random graphs

Dieter Mitsche (1) , Pawel Pralat (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 Department of Mathematics

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.

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Dieter Mitsche, Pawel Pralat. Revolutionaries and spies on random graphs. Combinatorics, Probability and Computing, 2013, 22, pp.417--432. ⟨10.1017/S0963548313000072⟩. ⟨hal-00923090⟩