Sampling Grid Colorings with Fewer Colors

  • Dimitris Achlioptas
  • Mike Molloy
  • Cristopher Moore
  • Frank Van Bussel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


We provide an optimally mixing Markov chain for 6-colorings of the square grid. Furthermore, this implies that the uniform distribution on the set of such colorings has strong spatial mixing. Four and five are now the only remaining values of k for which it is not known whether there exists a rapidly mixing Markov chain for k-colorings of the square grid.


Markov Chain Gibbs Measure Graph Coloring Free Boundary Condition Glauber Dynamic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Dimitris Achlioptas
    • 1
  • Mike Molloy
    • 2
  • Cristopher Moore
    • 3
  • Frank Van Bussel
    • 4
  1. 1.Microsoft Research
  2. 2.Dept of Computer ScienceUniversity of Toronto, and Microsoft Research
  3. 3.Computer Science DepartmentUniversity of New Mexico
  4. 4.Dept of Computer ScienceUniversity of Toronto

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