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Revolutionaries and Spies on Random Graphs

Published online by Cambridge University Press:  08 March 2013

DIETER MITSCHE  and
PAWEŁ PRAŁAT
DIETER MITSCHE
Affiliation:
Department of Mathematics, Ryerson University, Toronto, ON, Canada (e-mail: dmitsche@ryerson.ca, pralat@ryerson.ca)
PAWEŁ PRAŁAT
Affiliation:
Department of Mathematics, Ryerson University, Toronto, ON, Canada (e-mail: dmitsche@ryerson.ca, pralat@ryerson.ca)
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Abstract

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 σ(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 analysed completely for dense graphs (that is, graphs with average degree at least n1/2+ε for some ε > 0). For sparser graphs, some bounds are provided.

Keywords

Primary 05C80Secondary 05C5768R10
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 3 , May 2013 , pp. 417 - 432
Copyright
Copyright © Cambridge University Press 2013

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