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- W172109902 abstract "Let G be an n-node graph with maximum degree Δ. The Glauber dynamics for G, defined by Jerrum, is a Markov chain over the k-colorings of G. Many classes of G on which the Glauber dynamics mixes rapidly have been identified. Recent research efforts focus on the important case that Δ ≥ dlog2 n holds for some sufficiently large constant d. We add the following new results along this direction, where e can be any constant with 0 < e < 1. Let α ≈ 1.645 be the root of (1 − e − 1/x )2 + 2x e − 1/x = 2. If G is regular and bipartite and k ≥ (α + e)Δ, then the mixing time of the Glauber dynamics for G is O(nlogn).Let β ≈ 1.763 be the root of x = e 1/x . If the number of common neighbors for any two adjacent nodes of G is at most (frac{epsilon^{1.5}Delta}{360e}) and k ≥ (1 + e)βΔ, then the mixing time of the Glauber dynamics is O(nlogn)." @default.
- W172109902 created "2016-06-24" @default.
- W172109902 creator A5006379171 @default.
- W172109902 creator A5007033049 @default.
- W172109902 date "2012-01-01" @default.
- W172109902 modified "2023-09-27" @default.
- W172109902 title "Randomly Coloring Regular Bipartite Graphs and Graphs with Bounded Common Neighbors" @default.
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- W172109902 doi "https://doi.org/10.1007/978-3-642-35261-4_6" @default.
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