# A more rapidly mixing Markov chain for graph colorings

@article{Dyer1998AMR, title={A more rapidly mixing Markov chain for graph colorings}, author={Martin E. Dyer and Catherine S. Greenhill}, journal={Random Struct. Algorithms}, year={1998}, volume={13}, pages={285-317} }

We define a new Markov chain on (proper) k-colorings of graphs, and relate its convergence properties to the maximum degree Δ of the graph. The chain is shown to have bounds on convergence time appreciably better than those for the well-known Jerrum/Salas–Sokal chain in most circumstances. For the case k=2Δ, we provide a dramatic decrease in running time. We also show improvements whenever the graph is regular, or fewer than 3Δ colors are used. The results are established using the method of…

## 72 Citations

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