Catch Me If You Can: Cops and Robbers on Graphs
نویسنده
چکیده
Vertex pursuit games are widely studied by both graph theorists and computer scientists. Cops and Robbers is a vertex pursuit game played on a graph, where some set of agents (or Cops) attempts to capture a robber. The cop number is the minimum number of cops needed to win. While cop number of a graph has been studied for over 25 years, it is not well understood, and has few connections with existing graph parameters. In this survey, we highlight some of the main results on bounding the cop number, and discuss Meyniel’s conjecture on an upper bound for the cop number of connected graphs. We include a new proof of the fact that outerplanar graphs have cop number at most two.
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