The capture time of grids

Details The capture time of grids The capture time of grids

2010-08-26

arxiv.org/abs/1008.4424v2

Discrete Mathematics 311 (2011) pp. 102-105

Mathematics

Combinatorics

7 pages

Scientific paper

10.1016/j.disc.2010.10.002

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).

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