The spanning laceability on the faulty bipartite hypercube-like networks

摘要

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