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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