A Fast Distributed Algorithm for (Δ+1)-Edge-Coloring

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 Grebik and Pikhurko.

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