On Approximately Counting Colorings of Small Degree Graphs

@article{Bubley1999OnAC,
  title={On Approximately Counting Colorings of Small Degree Graphs},
  author={Russ Bubley and Martin E. Dyer and Catherine S. Greenhill and Mark Jerrum},
  journal={SIAM J. Comput.},
  year={1999},
  volume={29},
  pages={387-400}
}
We consider approximate counting of colorings of an n-vertex graph using rapidly mixing Markov chains. It has been shown by Jerrum and by Salas and Sokal that a simple random walk on graph colorings would mix rapidly, provided the number of colors k exceeded the maximum degree $\Delta$ of the graph by a factor of at least 2. We prove that this is not a necessary condition for rapid mixing by considering the simplest case of 5-coloring graphs of maximum degree 3. Our proof involves a computer… 

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