Constructing 2- and 3-connected graphs

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 $k\ge 4$ is also addressed.

arXiv commentThis paper has been withdrawn by the author following the finding of a significant shortcut in the paper of Barnette and Grünbaum titled "On Steinitz's theorem concerning convex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