  Reed conjectured that for every $\varepsilon>0$ and every integer $\Delta$,
there exists $g$ such that the fractional total chromatic number of every graph
with maximum degree $\Delta$ and girth at least $g$ is at most
$\Delta+1+\varepsilon$. The conjecture was proven to be true when $\Delta=3$ or
$\Delta$ is even. We settle the conjecture by proving it for the remaining
cases.
