Construction Sequences and Certifying 3-Connectedness

Jens M. Schmidt

Construction Sequences and Certifying 3-Connectedness

Data Structures and Algorithms 2010-02-03 v2 Discrete Mathematics

Authors: Jens M. Schmidt

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.

Keywords

planar graph drawing graph theory

Cite

@article{arxiv.0912.2561,
  title  = {Construction Sequences and Certifying 3-Connectedness},
  author = {Jens M. Schmidt},
  journal= {arXiv preprint arXiv:0912.2561},
  year   = {2010}
}