Cop and Robber Game and Hyperbolicity
Jérémie Chalopin, Victor D. Chepoi, Panos Papasoglu, Timothée Pecatte · SIAM Journal on Discrete Mathematics · 2014
In this note, we prove that all cop-win graphs $G$ in the game in which the robber and the cop move at different speeds $s$ and $s'$ with $s'0$, this establishes a new---game-theoretical---characterization of Gromov hyperbolicity. We also show that for weakly modular graphs the dependency between $\delta$ and $s$ is linear for any $s'