The robber strikes back

Abstract

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.

References in corpus (1)

• Meyniel's conjecture holds for random graphs

Cited by in corpus (3)

• A probabilistic version of the game of Zombies and Survivors on graphs
• Containment game played on random graphs: another zig-zag theorem
• Lazy Cops and Robbers played on Graphs