Regular connected bipancyclic spanning subgraphs of hypercubes

AbstractAn n-dimensional hypercube Qn is a Hamiltonian graph; in other words Qn (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, Qn (n≥3) contains a spanning subgraph which is k-regular, k-connected and bipancyclic. We also obtain the result that every mesh Pm×Pn (m,n≥2) is bipancyclic, which is used to prove the property above