Open Access
2007 Pursuit-Evasion in Models of Complex Networks
Anthony Bonato, Paweł Prałat, Changping Wang
Internet Math. 4(4): 419-436 (2007).


Pursuit-evasion games, such as the game of Cops and Robbers, are a simplified model for network security. In this game, cops try to capture a robber loose on the vertices of the network. The minimum number of cops required to win on a graph $G$ is its number. We present asymptotic results for the game of Cops and Robbers played in various stochastic network models, such as in $G(n,p)$ with nonconstant $p$ and in random power-law graphs. We find bounds for the cop number of $G(n,p)$ for a large range $p$ as a function of $n$. We prove that the cop number of random power-law graphs with $n$ vertices is asymptotically almost surely $\Theta(n)$. The cop number of the core of random power-law graphs is investigated, and it is proved to be of smaller order than the order of the core.


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Anthony Bonato. Paweł Prałat. Changping Wang. "Pursuit-Evasion in Models of Complex Networks." Internet Math. 4 (4) 419 - 436, 2007.


Published: 2007
First available in Project Euclid: 27 May 2009

zbMATH: 1206.68030
MathSciNet: MR2522951

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.4 • No. 4 • 2007
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