Hamiltonian laceability of bubble-sort graphs with edge faults

It is known that the n-dimensional bubble-sort graph B-n is bipartite, (n - 1)-regular, and has n! vertices. We first show that, for any vertex v, B-n - v has a hamiltonian path between any two vertices in the same partite set without v. Let F be a subset of edges of B-n. We next show that B-n - F has a hamiltonian path between any two vertices of different partite sets if vertical bar F vertical bar is at most n - 3. Then we also prove that B-n - F has a path of length n! - 2 between any pair of vertices in the same partite set. (C) 2007 Elsevier Inc. All rights reserved.