Faster 3-colouring algorithm for graphs of diameter 3
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917531996913664 |
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| author | Groenland, Carla Koerts, Hidde Spirkl, Sophie |
| author_facet | Groenland, Carla Koerts, Hidde Spirkl, Sophie |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13072 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Faster 3-colouring algorithm for graphs of diameter 3 Groenland, Carla Koerts, Hidde Spirkl, Sophie Combinatorics Discrete Mathematics 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]. |
| title | Faster 3-colouring algorithm for graphs of diameter 3 |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2601.13072 |