Geodesic
On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 805-817.

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The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn 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 ∈ Vi, i ∈ 0, 1, any edge e ∈ E(G − v), there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn is edge-hyper- Hamiltonian laceable.
Keywords: balanced hypercubes, hyper-Hamiltonian laceability, edge- hyper-Hamiltonian laceability 
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Cao, Jianxiang; Shi, Minyong; Feng, Lihua. On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 805-817. http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a2/

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