The balanced hypercube $BH_{ n}$, a variant of the hypercube, is a novel interconnection network for massive parallel systems. It is known that the balanced hypercube remains Hamiltonian after deleting at most $4n-5$ faulty edges if each vertex is incident with at least two edges in the resulting graph for all $n\geq2$. In this paper, we show that there exists a fault-free Hamiltonian cycle in $BH_{ n}$ for $n\ge 2$ with $\left | F \right |\le 5n-7$ if the degree of every vertex in $BH_{ n}-F$ is at least two and there exists no $f_{ 4}$-cycles in $BH_{ n}-F$, which improves some known results.
Categories: math.CO