The Game of Cop and Robbers
In the game of Cops and Robbers , there is a map consisting of nodes and edges.
- The cop and the robber are each on some node to begin with.
- The cop and the robber take turns to make moves.
- In each turn, the cop or the robber can either stay where he is, or go to a node that is connected by an edge.
The cop wins if he can manage to capture the robber , i.e. be in the same vertex as the robber.
Here are a few maps on which Cops and Robbers can be played:
On one of these maps, it is never possible for the cop to win if the robber plays well. Which one is it?
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In both maps B and C, the cop can be in a node where he can catch the crook no matter what move the crook makes. Only in map A the cop can't do that.