Corpus ID: 4780474

Rapid mixing of Glauber dynamics for colorings below Vigoda's 11/6 threshold

@article{Delcourt2018RapidMO,
  title={Rapid mixing of Glauber dynamics for colorings below Vigoda's 11/6 threshold},
  author={Michelle Delcourt and Guillem Perarnau and Luke Postle},
  journal={ArXiv},
  year={2018},
  volume={abs/1804.04025}
}
A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$-colorings of a graph $G$ on $n$ vertices with maximum degree $\Delta$ is rapidly mixing for $k \geq \Delta +2$. In FOCS 1999, Vigoda showed rapid mixing of flip dynamics with certain flip parameters on the set of proper $k$-colorings for $k > \frac{11}{6}\Delta$, implying rapid mixing for Glauber dynamics. In this paper, we obtain the first improvement beyond the $\frac{11}{6}\Delta… Expand
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