English

The capture time of the hypercube

Combinatorics 2013-08-16 v1 Discrete Mathematics

Abstract

In the game of Cops and Robbers, the capture time of a graph is the minimum number of moves needed by the cops to capture the robber, assuming optimal play. We prove that the capture time of the nn-dimensional hypercube is Θ(nlnn).\Theta (n\ln n). Our methods include a novel randomized strategy for the players, which involves the analysis of the coupon-collector problem.

Keywords

Cite

@article{arxiv.1308.3354,
  title  = {The capture time of the hypercube},
  author = {Anthony Bonato and William B. Kinnersley and P. Gordinowicz and P. Pralat},
  journal= {arXiv preprint arXiv:1308.3354},
  year   = {2013}
}
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