Perfect Sampling of graph k-colorings for k> 3Δ
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We give an algorithm for perfect sampling from the uniform distribution on proper k-colorings of graphs of maximum degree Δ which terminates with a sample in expected poly(k,n) time whenever k> 3Δ (here, n is the number of vertices in the graph). We provide a Coupling-from-the-Past based algorithm using the bounding chain approach. This approach was pioneered independently by Häggström & Nelander (Scand. J. Statist., 1999) and Huber (STOC 1998) (who used the approach to give a perfect sampling algorithm requiring k >Δ^2 + 2Δ for its expected running time to be a polynomial).
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