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Sci."],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:p> The balanced hypercube, [Formula: see text], is a variant of hypercube [Formula: see text]. Zhou et al. [Inform. Sci. 300 (2015) 20\u201327] proposed an interesting problem that whether there is a fault-free Hamiltonian cycle in [Formula: see text] 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 [Formula: see text] after no more than [Formula: see text] faulty edges occur if each vertex is incident with at least two fault-free edges for all [Formula: see text]. 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