• Corpus ID: 15734955

Beating the 2Δ bound for approximately counting colourings: a computer-assisted proof of rapid mixing

@inproceedings{Bubley1998BeatingT2,
  title={Beating the 2$\Delta$ bound for approximately counting colourings: a computer-assisted proof of rapid mixing},
  author={Russ Bubley and Martin E. Dyer and Catherine S. Greenhill},
  booktitle={SODA '98},
  year={1998}
}
We consider random walks on graph colourings of an nvertex graph. It has been shown by Jerrum and by Salas and Sokal that a simple random walk would mix rapidly provided the number of colours, k, exceeded the maximum degree A of the graph by a factor of at least 2. Lack of improvements on this bound led to a conjecture that k 2 2A was a natural barrier. We disprove this conjecture in the simplest case of 5-colouring graphs of maximum degree 3. Our proof involves a novel computer-assisted proof… 

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