Construction Sequences and Certifying 3-Connectedness

Jens M. Schmidt

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arXiv · 0912.2561

Construction Sequences and Certifying 3-Connectedness

Jens M. Schmidt

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Abstract

Tutte proved that every 3-connected graph on more than 4 nodes has a contractible edge. Barnette and Gruenbaum proved the existence of a removable edge in the same setting. We show that the sequence of contractions and the sequence of removals from G to the K_4 can be computed in O(|V|^2) time by extending Barnette and Gruenbaum's theorem. As an application, we derive a certificate for the 3-connectedness of graphs that can be easily computed and verified.

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Jens M. Schmidt. 2010-02-03. Construction Sequences and Certifying 3-Connectedness. https://arxiv.org/abs/0912.2561

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