3-Colouring Planar Graphs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916825552388096 |
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| author | Dujmović, Vida Morin, Pat Norin, Sergey Wood, David R. |
| author_facet | Dujmović, Vida Morin, Pat Norin, Sergey Wood, David R. |
| contents | We show that every $n$-vertex planar graph is 3-colourable with monochromatic components of size $O(n^{4/9})$. The best previous bound was $O(n^{1/2})$ due to Linial, Matoušek, Sheffet and Tardos [Combin. Probab. Comput., 2008]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 3-Colouring Planar Graphs Dujmović, Vida Morin, Pat Norin, Sergey Wood, David R. Combinatorics Discrete Mathematics We show that every $n$-vertex planar graph is 3-colourable with monochromatic components of size $O(n^{4/9})$. The best previous bound was $O(n^{1/2})$ due to Linial, Matoušek, Sheffet and Tardos [Combin. Probab. Comput., 2008]. |
| title | 3-Colouring Planar Graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2507.03163 |