Merris's anti-regular graph accessibility conjecture

Let $E_n$ be the degree anti-regular graph, meaning the unique connected graph whose vertex degrees attain every value from $1$ through $n-1$. Let $\omega(E_n)$ denote its minimum relative forest accessibility. Merris's conjecture.

$$\omega(E_n)=\frac{1}{2(n+1)}.$$

This conjecture identifies the minimum relative forest accessibility of the degree anti-regular graph. The supplied source evidence reports that it was disproved by a counterexample in Zhang's work.