Cames van Batenburg–de Joannis de Verclos–Kang–Pirot fractional chromatic conjecture

Let $n$ tend to infinity, and let $G$ be a triangle-free graph on $n$ vertices. Write $\chi_f(G)$ for its fractional chromatic number. Cames van Batenburg–de Joannis de Verclos–Kang–Pirot's fractional chromatic conjecture. Every such graph satisfies

$$\chi_f(G)\le(\sqrt{2}+o(1))\sqrt{\frac{n}{\ln n}}.$$

The paper confirms this conjecture using the connection with the local fractional Shearer conjecture established by Kelly and Postle. Thus the conjectured asymptotic upper bound is solved.