Conjectured upper bound for the saturation number of fullerene graphs

Let $F$ be a fullerene graph on $n$ vertices, and let $s(F)$ denote its saturation number, the minimum cardinality of a maximal matching in $F$.

Fullerene saturation-number conjecture. There is a constant $C$ such that

$$s(F)\leq \frac{n}{3}+C$$

for every fullerene graph $F$ on $n$ vertices.

The preceding lower and upper bounds are asymptotically equal, but the exact value of the saturation number remains open. This conjecture asserts that the upper bound differs from $n/3$ by at most an absolute constant.