On Counting Independent Sets in Sparse Graphs

@article{Dyer2002OnCI,
  title={On Counting Independent Sets in Sparse Graphs},
  author={M. Dyer and A. Frieze and M. Jerrum},
  journal={SIAM J. Comput.},
  year={2002},
  volume={31},
  pages={1527-1541}
}
We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree $\Delta$. The first implies that the Markov chain Monte Carlo technique is likely to fail if $\Delta \geq 6$. The second shows that no fully polynomial randomized approximation scheme can exist for $\Delta \geq 25$, unless $\mathrm{RP}=\mathrm{NP}$. 
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