Edge-Bipancyclicity of All Conditionally Faulty Hypercubes

In this paper, we consider the conditionally faulty hypercube Q(n) with n >= 2 that each vertices of Q(n) is incident with at least m fault-free edges, 2 <= m <= n-1. We shall generalize the limitation m >= 2 in all previous results of edge-bipancyclicity. For every integer m, under the hypothesis, we prove that Q(n) is (n-2)-edge-fault-tolerant edge-bipancyclic, and the results are optimal with respect to the number of edge faults tolerated. This improves some known results on edge-bipancyclicity of hypercubes.