Abstract
We prove that the Glauber dynamics on the k-colourings of a graph G on n vertices with girth 5 and maximum degree Δ ≥ 1000 log3 n mixes rapidly if k = qΔ and q > β where β= 1.645... is the root of 2-(1-e − 1/β)2 − 2βe − 1/β = 0.
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Lau, L.C., Molloy, M. (2006). Randomly Colouring Graphs with Girth Five and Large Maximum Degree. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_61
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DOI: https://doi.org/10.1007/11682462_61
Publisher Name: Springer, Berlin, Heidelberg
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