Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648801 | Discrete Mathematics | 2011 | 4 Pages |
Abstract
We consider the game of cops and robber played on the Cartesian product of two trees. Assuming the players play perfectly, it is shown that if there are two cops in the game, then the length of the game (known as the 2-capture time of the graph) is equal to half the diameter of the graph. In particular, the 2-capture time of the m×nm×n grid is proved to be ⌊m+n2⌋−1.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
A. Mehrabian,