A tight lower bound for the capture time of the Cops and Robbers game

Abstract 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 )...More