The robber strikes back
Anthony Bonato, Stephen Finbow, Przemysław Gordinowicz, Haidar Ali, William B. Kinnersley, Dieter Mitsche, Paweł Prałat, Ladislav Stacho · arXiv (Cornell University) · 2013
We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, then that cop is removed from the game. We study the minimum number of cops needed to capture a robber on a graph $G$, written $cc(G)$. We give bounds on $cc(G)$ in terms of the cop number of $G$ in the classes of bipartite graphs and diameter two, $K_{1,m}$-free graphs.