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arXiv · 2601.13072

Faster 3-colouring algorithm for graphs of diameter 3

Carla Groenland·Hidde Koerts·Sophie Spirkl
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Abstract

We show that given an $n$-vertex graph $G$ of diameter 3 we can decide if $G$ is $3$-colourable in time $2^{O(n^{2/3-\varepsilon})}$ for any $\varepsilon < 1/33$. This improves on the previous best algorithm of $2^{O((n\log n)^{2/3})}$ from Dębski, Piecyk and Rzążewski [Faster 3-coloring of small-diameter graphs, ESA 2021].

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Carla Groenland, Hidde Koerts, Sophie Spirkl. 2026-05-25. Faster 3-colouring algorithm for graphs of diameter 3. https://arxiv.org/abs/2601.13072

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