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Randomly coloring constant degree graphs

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4 Author(s)
Dyer, M. ; Sch. of Comput. Studies, Leeds Univ., UK ; Frieze, A. ; Hayes, T.P. ; Vigoda, E.

We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree Δ. We prove that the dynamics converges to a random coloring after O(n log n) steps assuming k ≥ k0 for some absolute constant k0, and either: (i) k/Δ > α* ≈ 1.763 and the girth g ≥ 5, or (ii) k/Δ > β* ≈ 1.489 and the girth g ≥ 6. Previous results on this problem applied when k = Ω(log n), or when k > 11 Δ/6 for general graphs.

Published in:

Foundations of Computer Science, 2004. Proceedings. 45th Annual IEEE Symposium on

Date of Conference:

17-19 Oct. 2004