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@?|V(G)|-1 and l-d(x,y)=0 (mod 2). We prove that the n-dimensional balanced hypercube BH"n 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.

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