A fast distributed algorithm for (Δ + 1)-edge-coloring

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...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series B 2022-01, Vol.152, p.319-352
Main Author: Bernshteyn, Anton
Format: Article
Language:English
Subjects:
Distributed algorithms
Edge-coloring
LOCAL model
Vizing's theorem
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Summary: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.
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2021.10.004