Planar graphs are 9/2-colorable

TL;DR

This paper proves that every planar graph can be colored with a fractional chromatic number at most 9/2, providing a new bound independent of the 4 Color Theorem.

Contribution

It establishes the first proof that planar graphs have a fractional chromatic number less than 5 without relying on the 4 Color Theorem.

Findings

Every planar graph has a 2-fold 9-coloring.

Fractional chromatic number of planar graphs is at most 9/2.

First proof of a universal constant less than 5 for fractional chromatic number of planar graphs.

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 $k$.