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