Edge-fault-tolerant bipanconnectivity of hypercubes

This paper shows that for any two distinct vertices u and v with distance d   in the hypercube QnQn (n⩾3n⩾3) with at most 2n-5 faulty edges and each vertex incident with least two fault-free edges, there exist fault-free uv  -paths of length ℓℓ in QnQn for every ℓℓ with d+4⩽ℓ⩽2n-1d+4⩽ℓ⩽2n-1 and ℓ-d≡0(mod2). This result improves some known results on edge-fault bipanconnectivity of hypercubes. The proof is based on the recursive structure of QnQn.