A fast distributed algorithm for (Δ + 1)-edge-coloring - Bernshteyn, Anton (Journal of combinatorial theory. Series B, 2022)
We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly(Δ,log⁡n) rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only Δ+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 Grebík and Pikhurko.