The capture time of grids
Combinatorics
2010-11-02 v2
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 x n grid is proved to be floor ((m+n-2)/2).
Cite
@article{arxiv.1008.4424,
title = {The capture time of grids},
author = {Abbas Mehrabian},
journal= {arXiv preprint arXiv:1008.4424},
year = {2010}
}
Comments
7 pages