Regular connected bipancyclic spanning subgraphs of hypercubes

An n-dimensional hypercube Q_n is a Hamiltonian graph; in other words Q_n (n≥2) contains a spanning subgraph which is 2-regular and 2-connected. In this paper, we explore yet another strong property of hypercubes. We prove that for any integer k with 3≤k≤n, Q_n (n≥3) contains a spanning subgraph which is k-regular, k-connected and bipancyclic. We also obtain the result that every mesh P_m×P_n (m,n≥2) is bipancyclic, which is used to prove the property above.