Bipanconnectivity of balanced hypercubes

The balanced hypercube, proposed by Wu and Huang, is a variant of the hypercube network. In this paper, paths of various lengths are embedded into balanced hypercubes. A bipartite graph G is bipanconnected if, for two arbitrary nodes x and y of G with distance d(x, y), there exists a path of length l between x and y for every integer l with d(x, y) <= l <= vertical bar V (G)vertical bar - 1 and l - d(x, y) 0 (mod 2). We prove that the n-dimensional balanced hypercube BHn is bipanconnected for all n >= 1. This result is stronger than that obtained by Xu et al. which shows that the balanced hypercube is edge-bipancyclic and Hamiltonian laceable. (C) 2010 Elsevier Ltd. All rights reserved.