Hamiltonian cycles of balanced hypercube with more faulty edges

The balanced hypercube BHn, 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 > 2. In this paper, we show that there still exists a Hamiltonian cycle in BHn for n > 2 after deleting a set F of edges with | F | <= 5n - 7 if the degree of every vertex in BHn - F is at least two and there exists no f4-cycles in BHn - F, which improves some known results.(c) 2023 Elsevier B.V. All rights reserved.