Vertex pursuit games in stochastic network models

  • Authors:

  • Anthony Bonato;Paweł Prałat;Changping Wang

  • Affiliations:

  • Wilfrid Laurier University, Waterloo, Canada;Dalhousie University, Halifax, Canada;Wilfrid Laurier University, Waterloo, Canada

  • Venue:
  • CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
  • Year:
  • 2007

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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.