Chasing robbers on random graphs: Zigzag theorem

Authors:
Tomasz Łuczak;Paweł Prałat
Affiliations:
Adam Mickiewicz University, Collegium Mathematicum, 61-614 Poznań, Poland;Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310
Venue:
Random Structures & Algorithms
Year:
2010

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Abstract

In this paper, we study the vertex pursuit game of Cops and Robbers where cops try to capture a robber on the vertices of the graph. The minimum number of cops required to win on a given graph G is the cop number of G. We present asymptotic results for the game of Cops and Robber played on a random graph G(n,p) for a wide range of p = p(n). It has been shown that the cop number as a function of an average degree forms an intriguing zigzag shape. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010 Supported by the Foundation for Polish Science.