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Abstract

We study the Glauber dynamics Markov chain for k-colourings of trees with maximum degree Δ. For k ≥ 3, we show that the mixing time on every tree is at most n O(1 + Δ/(k logΔ)). This bound is tight up to the constant factor in the exponent, as evidenced by the complete tree. Our proof uses a weighted canonical paths analysis and a variation of the block dynamics that exploits the differing relaxation times of blocks.

Keywords

Planar Graph Maximum Degree Boundary Node Glauber Dynamic Proper Colouring 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Brendan Lucier
    • 1
  • Michael Molloy
    • 1
  • Yuval Peres
    • 2
  1. 1.Dept of Computer ScienceUniversity of TorontoCanada
  2. 2.Microsoft ResearchUSA

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