Hamiltonian cycles of balanced hypercube with disjoint faulty edges

The balanced hypercube BH n , a variant of the hypercube, is a novel interconnection network topology for massive parallel systems. It is showed in [Theor. Comput. Sci. 947 (2023) 113708] that for any edge subset F of BH n there exists a fault -free Hamiltonian cycle in BH n - F for n >= 2 with | F | <= 5 n - 7 if the degree of every vertex in BH n - F is at least two and there exist no f 4 -cycles in BH n - F . In this paper, we consider the existence of Hamiltonian cycles of BH n when F is a matching (a set of disjoint edges), and show that each edge e is not an element of F lies on a fault -free Hamiltonian cycle of BH n - F with n >= 2. The number of faulty edges in F can be up to 2 2 n -1 , which is exponential to the dimension n .