Edge Fault-Tolerant Strong Hamiltonian Laceability of Balanced Hypercubes

The balanced hypercube BHn, proposed by Wu and Huang, is a new variation of hypercube. A Hamiltonian bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path between two arbitrary vertices from different partite sets. A Hamiltonian laceable graph G is strongly Hamiltonian laceable if there is a path of length vertical bar V (G)vertical bar-2 between any two distinct vertices of the same partite set. A graph G is called k-edge-fault strong Hamiltonian laceable, if G is strong Hamiltonian laceable for any edge-fault set F with vertical bar F vertical bar <= k. It has been proved that the balanced hypercube BHn is strong Hamiltonian laceable. In this paper, we improve the above result and prove that BHn is (n - 1) strong Hamiltonian laceable.