Construction Sequences and Certifying 3-Connectedness

Jens M. Schmidt
Given two $3$-connected graphs $G$ and $H$, a \emph{construction sequence} constructs $G$ from $H$ (e.\,g. from the $K_4$) with three basic operations, called the \emph{Barnette-Gr\"unbaum operations}. These operations are known to be able to construct all $3$-connected graphs. We extend this result by identifying every intermediate graph in the construction sequence with a subdivision in $G$ and showing under some minor assumptions that there is still a construction sequence to $G$ when we start from...