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arXiv · 2407.04887

A linear-time algorithm for $(1+\epsilon)\Delta$-edge-coloring

Anton Bernshteyn·Abhishek Dhawan
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Abstract

We present a randomized algorithm that, given a constant $\epsilon > 0$, outputs a proper $(1+\epsilon)\Delta$-edge-coloring of an $m$-edge simple graph $G$ of maximum degree $\Delta \geq 1/\epsilon$ in $O(m)$ time with high probability. This is the first linear-time algorithm for this problem covering the full range of possible values of $\Delta$. Indeed, even for edge-coloring with $2\Delta - 1$ colors (i.e., meeting the "greedy" bound), no such linear-time algorithm has been previously known.

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Anton Bernshteyn, Abhishek Dhawan. 2024-07-05. A linear-time algorithm for $(1+\epsilon)\Delta$-edge-coloring. https://arxiv.org/abs/2407.04887

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