Abstract
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 B H 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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