The capture time of grids |
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| Authors: | A Mehrabian |
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| Institution: | aDepartment of Computer Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran |
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| 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×n grid is proved to be  . |
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| Keywords: | Cops and Robber game Capture time Cartesian products Grids |
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