We prove that every planar triangle-free graph on $n$ vertices has fractional chromatic number at most $3-\frac{1}{n+1/3}$.
3-coloring triangle-free planar graphs with a precolored 8-cycle
Fine structure of 4-critical triangle-free graphs II. Planar triangle-free graphs with two precolored 4-cycles
The fractional chromatic number of $K_Δ$-free graphs
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