Clique-local fractional Reed conjecture

Let $G$ be a simple graph, let $\mathcal C(G)$ be the set of maximal cliques of $G$, and let $\gamma'_\ell(v)$ denote the fractional Reed bound of the induced graph on the closed neighbourhood of $v$.

Clique-local fractional Reed conjecture. Every graph $G$ satisfies

$$\chi_f(G)\leq\max_{C\in\mathcal C(G)}\frac{1}{|C|}\sum_{v\in C}\gamma'_\ell(v).$$

This conjecture pushes the locality further by averaging the single-vertex fractional bounds over maximal cliques. The paper presents it as a proposed fractional strengthening; no general resolution is given.