Abstract:Let G be a cyclically 5-connected cubic graph with a 5-edge-cut separating G into two cyclic components G 1 and G 2 . We prove that each component G i can be completed to a cyclically 5-connected cubic graph by adding three vertices, unless G i is a cycle of length five. Our work extends similar results by Andersen et al. for cyclic connectivity 4 from 1988.
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