Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777523 | Journal of Combinatorial Theory, Series A | 2017 | 12 Pages |
Abstract
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 nÃn grid is expâ¡(Ω(logâ¡n/logâ¡logâ¡n)).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Paul Balister, Amy Shaw, Béla Bollobás, Bhargav Narayanan,