  The balanced hypercube, $BH_n$, is a variant of hypercube $Q_n$. Zhou et al.
[Inform. Sci. 300 (2015) 20-27] proposed an interesting problem that whether
there is a fault-free Hamiltonian cycle in $BH_n$ with each vertex incident to
at least two fault-free edges. In this paper, we consider this problem and show
that each fault-free edge lies on a fault-free Hamiltonian cycle in $BH_n$
after no more than $4n-5$ faulty edges occur if each vertex is incident with at
least two fault-free edges for all $n\ge 2$. Our result is optimal with respect
to the maximum number of tolerated edge faults.
