Merris's algebraic-connectivity conjecture for graph accessibility

Let $G$ be a graph on $n$ vertices. Let $a(G)$ denote its algebraic connectivity, and let $\omega(G)$ denote the minimum entry of its matrix of relative forest accessibilities. Merris's conjecture.

$$a(G) \geq 2(n+1)\omega(G).$$

This conjecture relates algebraic connectivity to the smallest relative forest accessibility of a graph. It was disproved by a counterexample given in Zhang's work.