Cops and Robbers on a Cube
On Friday, October 21, 2011, the York College Tensor Scholars Program hosted a talk by Dr. Kerry Ojakian from the Department of Mathematics at Queens College, CUNY. Dr. Ojakian’s talk focused on the game Cops and Robbers on a Cube.
This is a two-player game, played with an undirected graph. The cops’ objective is to catch the robber while the robber is trying to evade being caught. To begin the game, the cops choose any vertices to occupy, and then the robber chooses a vertex to occupy.
The players then take turns, at each turn remaining stationary or moving to an adjacent vertex. The cops win if they catch the robber, that is, if they ever occupy the same vertex as the robber; the robber wins if he can avoid being caught indefinitely. The talk was well received by those in attendance.