Monotonicity conjecture for the fractional chromatic deficit

For each $\Delta\geq 3$, define $f(\Delta)$ as the best universal fractional-coloring deficit for graphs of maximum degree $\Delta$ in the paper's setting. Monotonicity conjecture. One has

$$f(\Delta)\leq f(\Delta+1).$$

This asks whether the fractional chromatic deficit is nondecreasing with the maximum degree and is identified in the paper as a major open question.