Construction Sequences and Certifying 3-Connectedness

Jens M. Schmidt 1, *
* Corresponding author
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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Conference papers
Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.633-644, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science
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Jens M. Schmidt. Construction Sequences and Certifying 3-Connectedness. Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.633-644, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science. 〈inria-00455813〉

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