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A Tight Lower Bound for the Capture Time of the Cops and Robbers Game * †

2017
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licensed under Creative Commons License CC-BY 44th International Colloquium on Automata, Languages, and Programming
*
unpublished

For the game of Cops and Robbers, it is known that in 1-cop-win graphs, the cop can capture the robber in O(n) time, and that there exist graphs in which this capture time is tight. When k ≥ 2, a simple counting argument shows that in k-cop-win graphs, the capture time is at most O(n k+1), however, no non-trivial lower bounds were previously known; indeed, in their 2011 book, Bonato and Nowakowski ask whether this upper bound can be improved. In this paper, the question of Bonato and Nowakowski

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