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arXiv · 2605.07774

Beyond Brooks: $(\Delta-1)$-Coloring in Semi-Streaming

Maxime Flin·Magnús M. Halldórsson
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Abstract

Reed [J.~Comb.~Theory B, 1999] showed that graphs of maximum degree $\Delta \geq 10^{14}$ without $\Delta$-cliques are $(\Delta-1)$-colorable. We design a one-pass semi-streaming algorithm for computing such a coloring. Additionally, we prove that any one-pass $(\Delta-k)$-coloring algorithm for $0\leq k < (\Delta+1)/2$ requires $\Omega(n(k+1))$ space.

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Maxime Flin, Magnús M. Halldórsson. 2026-05-08. Beyond Brooks: $(\Delta-1)$-Coloring in Semi-Streaming. https://arxiv.org/abs/2605.07774

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