Doš​lić–Vukićević explicit conjecture for bipartizing fullerenes

Let $H$ be a fullerene graph with $n$ vertices, and let $b(H)$ be the minimum number of edges whose removal makes $H$ bipartite. Doš​lić–Vukićević explicit conjecture.

$$b(H)\leq \sqrt{12n/5}.$$

This is presented as a stronger form of the asymptotic conjecture that $b(H)=O(\sqrt{|V(H)|})$; no resolution is given in the supplied text.