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.
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