Hamiltonian cycle embedding for fault tolerance in balanced hypercubes

The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network. Yang proposed that fault tolerance of balanced hypercube BHn is an important issue in parallel computing which needs further study (Yang, 2010) [24]. In this paper, we prove that there exists a fault-free Hamiltonian path between any two adjacent vertices in BHn with 2n-2 faulty edges. As a corollary, we derive that for any fault-free edge e, there exists a fault-free Hamiltonian cycle containing e in BHn with 2n-2 faulty edges which is optimal in the sense of the number of faulty edges.