  For each finite simple graph $G$, Aharoni, Berger and Ziv consider a
recursively defined number $\psi (G) \in \mathbb{Z}\cup \{+ \infty \}$ which
gives a lower bound for the topological connectivity of the independence
complex $I_G$. They conjecture that this bound is optimal for every graph. We
use a result of recursion theory to give a short disproof of this claim.
