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arXiv · 2107.09756

Decomposition of cubic graphs with cyclic connectivity 5

Edita Máčajová·Jozef Rajník
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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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Edita Máčajová, Jozef Rajník. 2021-07-20. Decomposition of cubic graphs with cyclic connectivity 5. https://arxiv.org/abs/2107.09756

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