Edge-pancyclicity and Hamiltonian laceability of the balanced hypercubes

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

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