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- W803544166 abstract "Cops and Robber is a pursuit and evasion game played on graphs that has received much attention. We consider an extension of Cops and Robber, distance k Cops and Robber, where the cops win if they are distance at most k from the robber in G. The cop number of a graph G is the minimum number of cops needed to capture the robber in G. The distance k analogue of the cop number, written ck(G), equals the minimum number of cops needed to win at a given distance k. We supply a classification result for graphs with bounded ck(G) values and develop an O(n2s+3) algorithm for determining if ck(G) ≤ s. In the case k = 0, our algorithm is faster than previously known algorithms. Upper and lower bounds are found for ck(G) in terms of the order of G. We prove that[EQUATION]where ck(n) is the maximum of ck(G) over all n-node connected graphs." @default.
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- W803544166 date "2009-01-03" @default.
- W803544166 modified "2023-09-23" @default.
- W803544166 title "Pursuit and evasion from a distance: algorithms and bounds" @default.
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