Cycle embedding in crossed cubes with conditional edge faults

Crossed cubes are important variants of hypercubes. In this paper, we consider the cycle embedding problem in crossed cubes with conditional edge faults. We show that there exist cycles of all lengths from 4 to 2
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in an n-dimensional crossed cube with ≤ 2n - 7 edge faults in which each vertex is incident with at least two healthy edges for n ≥ 5.