Vertex Pursuit Games in Stochastic Network Models

Abstract. Random graphs with given expected degrees G(w) were introduced by Chung and Lu so as to extend the theory of classical G(n, p) random graphs to include random power law graphs. We investigate asymptotic results for the game of Cops and Robber played on G(w) and G(n, p). Under mild conditions on the degree sequence w, an asymptotic lower bound for the cop number of G(w) is given. We prove that the cop number of random power law graphs with n vertices is asymptotically almost surely Θ(n). We derive concentration results for the cop number of G(n, p) for p as a function of n.

• Type: Conference
• Year: 2007
• Where: CAAN
• Authors: Anthony Bonato, Pawel Pralat, Changping Wang
• Keywords: CAAN 2007, Cop Number, Discrete Geometry, Power Law Graphs, Random Power Law