Catching a fast robber on the grid

Paul Balister, Amy Shaw, Béla Bollobás, Bhargav Narayanan

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study the problem of cops and robbers on the grid where the robber is allowed to move faster than the cops. It is well known that two cops are necessary and sufficient to catch the robber on any finite grid when the robber has unit speed. Here, we prove that if the speed of the robber exceeds a sufficiently large absolute constant, then the number of cops needed to catch the robber on an n×n grid is exp⁡(Ω(log⁡n/log⁡log⁡n)).

Original languageEnglish (US)
Pages (from-to)341-352
Number of pages12
JournalJournal of Combinatorial Theory. Series A
StatePublished - Nov 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


  • Cops and robbers
  • Games on graphs


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