The cover time of the giant component of a random graph

  • Authors:
  • Colin Cooper;Alan Frieze

  • Affiliations:
  • Department of Computer Science, King's College, University of London, London WC2R 2LS, UK;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2008

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Abstract

We study the cover time of a random walk on the largest component of the random graph Gn,p. We determine its value up to a factor 1 + o(1) whenever np = c 1, c = O(lnn). In particular, we show that the cover time is not monotone for c = Θ(lnn). We also determine the cover time of the k-cores, k ≥ 2. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008