Edge Fault-Tolerant Strong Hamiltonian Laceability of Balanced Hypercubes

Abstract

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 [Formula: see text] between any two distinct vertices of the same partite set. A graph G is called k-edge-fault strong Hamiltonian laceable, if G – F is strong Hamiltonian laceable for any edge-fault set F with [Formula: see text]. 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)-edge-fault strong Hamiltonian laceable.