Let T be a tree on n vertices and with maximum degree . We show that for the Glauber dynamics for k‐edge‐ colorings of T mixes in polynomial time in n. The bound on the number of colors is best possible as the chain is not even ergodic for . Our proof uses a recursive decomposition of the tree into subtrees; we bound the relaxation time of the original tree in terms of the relaxation time of its subtrees using block dynamics and chain comparison techniques. Of independent interest, we also introduce a monotonicity result for Glauber dynamics that simplifies our proof.

中文翻译：

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树木边缘着色的格劳伯动力学

设T为n个顶点上最大度数的树。我们证明了对于G多项式时间中n的T混合的k边缘着色的Glauber动力学。颜色的界限是最好的，因为链甚至都不是遍历的。我们的证明使用了将树递归分解为子树的方法。我们使用块动力学和链比较技术根据原始树的子树的松弛时间来限制原始树的松弛时间。对于独立利益，我们还为Glauber动力学引入了单调性结果，从而简化了我们的证明。