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.

翻译：我们在 LOCAL 模型中展示了一种确定式分布式算法, 该算法找到一个适当的 $ (\ Delta + 1), 以$\ mathrm {poly} (\ Delta,\ log n) 圆为最大度的 $\ Delta$ (\ Delta,\ log n) 顶端图形 。 这是第一个使用$\ Delta + 1美元的非三端分布色谱算法( 匹配 Vizing 理论的约束值 ) 。 我们的方法来源于最近由 Greb\ ik 和 Pikhurko 提供的可测量的 Vizing 定理版本的证据 。