Fault-tolerant bipancyclicity of faulty hypercubes under the generalized conditional-fault model

Let F _v be a set of faulty nodes in an n-dimensional hypercube, denoted by Q _n. Also, let F _e be a set of faulty edges in which at least one end-node of each edge is faulty. An edge in Q _n is said to be critical if it is either fault-free or in F _e. In this paper, we prove that, for up to 2n-4 faulty nodes and/or edges, an n-dimensional hypercube contains a fault-free cycle of every even length from 4 to 2 ⁿ-2|F _v| in which each node is incident to at least two critical edges. Our result improves on the previously best known results reported in the literature.