  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.
