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The capture time of grids

Mehrabian, A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2010.10.002
  3. Publisher: 2011
  4. Abstract:
  5. 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 ⌊m+n2⌋-1
  6. Keywords:
  7. Capture time ; Cartesian products ; Cops and Robber game ; Grids
  8. Source: Discrete Mathematics ; Volume 311, Issue 1 , January , 2011 , Pages 102-105 ; 0012365X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0012365X10003808