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arXiv · 2006.15703

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

Anton Bernshteyn
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Abstract

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 $\mathrm{poly}(Δ, \log n)$ 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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Anton Bernshteyn. 2021-03-04. A Fast Distributed Algorithm for $(Δ+ 1)$-Edge-Coloring. https://arxiv.org/abs/2006.15703

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