  We show that the probability that a simple random walk covers a finite,
bounded degree graph in linear time is exponentially small.
  More precisely, for every D and C, there exists a=a(D,C)>0 such that for any
graph G, with n vertices and maximal degree D, the probability that a simple
random walk, started anywhere in G, will visit every vertex of G in its first
Cn steps is at most exp(-an).
  We conjecture that the same holds for a=a(C)>0 that does not depend on D,
provided that the graph G is simple.
