Edge-pancyclicity and Hamiltonian laceability of the balanced hypercubes

The balanced hypercube BHn is a variant of the hypercube Qn. Huang and Wu proved that BHn has better properties than Qn with the same number of links and processors. In particularly, they showed that there exists a cycle of length 2l in BHn for all l, 2 ⩽ l ⩽ 2n. In this paper, we improve this result by showing that BHn is edge-pancyclic, which means that for arbitrary edge e, there exists a cycle of even length from 4 to 22n containing e in BHn. We also show that the balanced hypercubes are Hamiltonian laceable.