Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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TWO REMARKS ON THE GAME OF COPS AND ROBBERS

  • Received : 2019.01.27
  • Accepted : 2019.11.19
  • Published : 2020.01.31
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Abstract

We discuss two unrelated topics regarding Cops and Robbers, a well-known pursuit-evasion game played on a simple graph. First, we address a recent question of Breen et al. and prove the PSPACE-completeness of the cop throttling number, that is, the minimal possible sum of the number k of cops and the number capt(k) of moves that the robber can survive against k cops under the optimal play of both sides. Secondly, we revisit a teleporting version of the game due to Wagner; we disprove one of his conjectures and suggest a new related research problem.

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References

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