SHGH conjecture for special divisors on blow-ups of the plane

Let $S$ be the blow-up of $s$ general points of $\mathbb P^2$, let $F$ be a divisor on $S$, and let an exceptional curve mean a smooth rational curve $E$ with $E^2=-1$. SHGH conjecture. If

$$h^0(S,\mathcal O_S(F))>0\qquad\text{and}\qquad h^1(S,\mathcal O_S(F))>0,$$

then there is an exceptional curve $E$ on $S$ such that

$$F\cdot E\leq -2.$$

This is the divisor-theoretic formulation of the Segre–Harbourne–Gimigliano–Hirschowitz conjecture given in the source. Its resolution status is not specified in the supplied text.