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The balanced hypercube $BH_{n}$, a variant of the hypercube, is a novelinterconnection network for massive parallel systems. It is known that thebalanced hypercube remains Hamiltonian after deleting at most $4n-5$ faultyedges if each vertex is incident with at least two edges in the resulting graphfor all $n\geq2$. In this paper, we show that there exists a fault-freeHamiltonian cycle in $BH_{n}$ for $n\ge 2$ with $\left | F \right |\le 5n-7$ ifthe 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.

Hamiltonian cycles of balanced hypercube with more faulty edges