Planar graphs are 9/2-colorable

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 $\frac{9}{2}$. 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 $k$.

12 pages, 6 figures; following the suggestion of an editor, we split the original version of this paper into two papers: one is the current version of this paper, and the other is "Planar graphs have Independence Ratio at least 3/13" (also available on the arXiv)