Fault-tolerant-prescribed hamiltonian laceability of balanced hypercubes

Given a bipartite graph G with bipartition (X, Y), let F subset of E(G) be a set of faulty edges and let L be a linear forest in G - F such that vertical bar F vertical bar + vertical bar E(L)vertical bar <= k. Let u epsilon X and v epsilon Y be any two vertices such that none of the paths in L has u or v as internal vertices or both of them as end vertices. G is said to be k-fault-tolerant-prescribed hamiltonian laceable if G - F admits a hamiltonian path between u and v passing through L. Balanced hypercubes are candidate interconnection networks of multiprocessor systems. In this paper, we prove that the n-dimensional balanced hypercube is (n - 1)-fault-tolerant-prescribed hamiltonian laceable. (C) 2019 Elsevier B.V. All rights reserved.