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arXiv · 2507.03163

3-Colouring Planar Graphs

Vida Dujmović·Pat Morin·Sergey Norin·David R. Wood
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Abstract

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].

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Vida Dujmović, Pat Morin, Sergey Norin, David R. Wood. 2026-07-16. 3-Colouring Planar Graphs. https://arxiv.org/abs/2507.03163

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