Constructing 2- and 3-connected graphs

Jonathan McLaughlin

Constructing 2- and 3-connected graphs

Combinatorics 2015-12-01 v2

Authors: Jonathan McLaughlin

Abstract

This work re-examines a classical construction of a 2-connected (simple) graph where every intermediate graph is 2-connected before detailing an analogous construction for 3-connected graphs which requires a graph equivalence relation $\sim_2$ and a related concept of the $\sim_2$ -core of a graph. The case of $k$ -connected graphs for $k\geq 4$ is also addressed.

Keywords

graph connectivity graph theory knot theory

Cite

@article{arxiv.1307.3129,
  title  = {Constructing 2- and 3-connected graphs},
  author = {Jonathan McLaughlin},
  journal= {arXiv preprint arXiv:1307.3129},
  year   = {2015}
}

Comments

This paper has been withdrawn by the author following the finding of a significant shortcut in the paper of Barnette and Gr\"unbaum titled "On Steinitz's theorem concerning convex $3$-polytopes and some properties of $3$-connected graphs"

Constructing 2- and 3-connected graphs

Abstract

Keywords

Cite

Comments

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