On 3-Regular Bipancyclic Subgraphs of Hypercubes

The n-dimensional hypercube Qn is bipancyclic; that is, it contains a cycle of every even length from 4 to 2n. In this paper, we prove that Qn (n≥3) contains a 3-regular, 3-connected, bipancyclic subgraph with l vertices for every even l from 8 to 2n except 10.