We present a deterministic distributed algorithm in the LOCAL model that finds a proper $(\Delta + 1)$-edge-coloring of an $n$-vertex graph of maximum degree $\Delta$ in $\mathrm{poly}(\Delta, \log n)$ rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only $\Delta+1$ colors (matching the bound given by Vizing's theorem). Our approach is inspired by the recent proof of the measurable version of Vizing's theorem due to Greb\'ik and Pikhurko.

中文翻译：

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$(\Delta + 1)$-Edge-Coloring 的快速分布式算法

我们在 LOCAL 模型中提出了一种确定性分布式算法，该算法在 $\mathrm{poly}(\ Delta，\log n)$ 轮次。这是第一个仅使用 $\Delta+1$ 颜色的非平凡分布式边缘着色算法（与 Vizing 定理给出的界限匹配）。我们的方法的灵感来自于最近由 Greb\'ik 和 Pikhurko 提出的 Vizing 定理的可测量版本的证明。