# 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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#### 8 Citations

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