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arXiv · 1410.7233

Planar graphs are 9/2-colorable

Daniel W. Cranston·Landon Rabern
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Abstract

We show that every planar graph $G$ has a 2-fold 9-coloring. In particular, this implies that $G$ has fractional chromatic number at most $\frac92$. This is the first proof (independent of the 4 Color Theorem) that there exists a constant $k<5$ such that every planar $G$ has fractional chromatic number at most $k$.

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Daniel W. Cranston, Landon Rabern. 2016-09-20. Planar graphs are 9/2-colorable. https://arxiv.org/abs/1410.7233

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