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The Cover Time of Cartesian Product Graphs

  • Mohammed Abdullah
  • Colin Cooper
  • Tomasz Radzik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

Let P = GH be the cartesian product of graphs G,H. We relate the cover time COV[P] of P to the cover times of its factors. When one of the factors is in some sense larger than the other, its cover time dominates, and can become of the same order as the cover time of the product as a whole. Our main theorem effectively gives conditions for when this holds. The probabilistic technique which we introduce, based on the blanket time, is more general and may be of independent interest, as might some of our lemmas.

Keywords

Random walks cover time blanket time effective resistance cartesian product graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mohammed Abdullah
    • 1
  • Colin Cooper
    • 1
  • Tomasz Radzik
    • 1
  1. 1.Department of Computer ScienceKing’s College LondonUK

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