The spanning laceability on the faulty bipartite hypercube-like networks

Abstract

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. (C) 2013 Elsevier Inc. All rights reserved.