The spanning laceability on the faulty bipartite hypercube-like networks

A w  -container C(u,v)C(u,v) of a graph G is a set of w-disjoint paths joining u to v. A w-container of G   is a w∗w∗-container if it contains all the nodes of V(G)V(G). A bipartite graph G   is w∗w∗-laceable if there exists a w∗w∗-container between any two nodes from different parts of G. Let n and k   be any two positive integers with n⩾2n⩾2 and k⩽nk⩽n. In this paper, we prove that n-dimensional bipartite hypercube-like graphs are f  -edge fault k∗k∗-laceable for every f⩽n-2f⩽n-2 and f+k⩽nf+k⩽n.