Conditional fault-tolerant edge-bipancyclicity of hypercubes with faulty vertices and edges

• Consider hypercubes with mixed faulty edges and faulty vertices under conditional-fault model.
• Improve the previous results about the fault-tolerant edge-bipancyclicity of hypercubes.
• Give an affirmative answer for a problem proposed by Yang et al. (2016).

Let F be a faulty set in an n  -dimensional hypercube QnQn such that in Qn−FQn−F each vertex is incident to at least two edges, and let fvfv, fefe be the numbers of faulty vertices and faulty edges in F  , respectively. In this paper, we consider the fault-tolerant edge-bipancyclicity of hypercubes. It is shown that each edge in Qn−FQn−F for n≥3n≥3 lies on a fault-free cycle of any even length from 6 to 2n−2fv2n−2fv if fv+fe≤2n−5fv+fe≤2n−5. This gives an answer for a problem proposed by Yang et al. (2016) [33].