Randomly coloring sparse random graphs with fewer colors than the maximum degree

  • Authors:

  • Martin Dyer;Abraham D. Flaxman;Alan M. Frieze;Eric Vigoda

  • Affiliations:

  • School of Computing, University of Leeds, Leeds LS2 9JT, UK;Department of Mathematics, Carnegie Mellon University, Pittsburgh, Pennsylvania;Department of Mathematics, Carnegie Mellon University, Pittsburgh, Pennsylvania;Department of Computer Science, University of Chicago, Chicago, Illinois

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2006

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Abstract

We analyze Markov chains for generating a random k-coloring of a random graph Gn,d/n. When the average degree d is constant, a random graph has maximum degree Θ(log n/log log n), with high probability. We show that, with high probability, an efficient procedure can generate an almost uniformly random k-coloring when k = Θ(log log n/log log log n), i.e., with many fewer colors than the maximum degree. Previous results hold for a more general class of graphs, but always require more colors than the maximum degree. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006