International audienceIn the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G = (V , E). The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) and Quilliot (1983) characterized the cop-win graphs as dismantlable graphs. In this talk, we will characterize in a similar way the class CWFR(s, s′ ) of cop-win graphs in the game in which the cop and the robber move at different speeds s′ and s, s′ ≤ s. We also establish some connections between cop-win graphs for this game with s′ 1. We characterize the graphs which are k-winnable for any value of k
