Cop-Win Graphs with Maximal Capture-Time
نویسنده
چکیده
Cop and robber is a two-player vertex-pursuit combinatorial game where the players stand on the vertices of a graph and alternate in moving to adjacent vertices. The cop wins when he captures the robber, robber’s goal is to avoid capture. The game has been studied in various modifications, many of which have an interesting relationship to certain well-known graph parameters, such as treewidth. In this paper we present the matching upper bound n − 4 for the maximum length of a cop and robber game (the capture-time) on a cop-win graph of order n. We analyse the structure of the class of all graphs attaining this maximum and describe an inductive construction of the entire class. We conclude our results with an exponential lower bound on the size of this class.
منابع مشابه
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