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Construction Sequences and Certifying 3-connectivity

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Abstract

Tutte proved that every 3-vertex-connected graph G on more than 4 vertices has a contractible edge. Barnette and Grünbaum 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 K 4 can be computed in O(|V|2) time by extending Barnette’s and Grünbaum’s theorem. As an application, we derive a certificate for the 3-vertex-connectivity of graphs that can be easily computed and verified.

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Authors and Affiliations

  1. Dept. of Computer Science, Freie Universität Berlin, Berlin, Germany

    Jens M. Schmidt

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  1. Jens M. Schmidt
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Correspondence to Jens M. Schmidt.

Additional information

This research was supported by the Deutsche Forschungsgemeinschaft within the research training group “Methods for Discrete Structures” (GRK 1408) and is an extended version of [13].

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Schmidt, J.M. Construction Sequences and Certifying 3-connectivity. Algorithmica 62, 192–208 (2012). https://doi.org/10.1007/s00453-010-9450-9

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  • DOI: https://doi.org/10.1007/s00453-010-9450-9

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