On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes

The balanced hypercube BH_n, defined by Wu and Huang, is a variant of the hypercube network Q_n, and has been proved to have better properties than Q_n with the same number of links and processors. For a bipartite graph G = (V₀ ∪ V₁,E), we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ V_i, i ∈ {0, 1}, any edge e ∈ E(G − v), there is a Hamiltonian path containing e in G − v between any two vertices of V_1−i. In this paper, we prove that BH_n is edge-hyper- Hamiltonian laceable.