A definition of "separator" is the following: Let $G$ is an $n$-vertex graph, then $S\subseteq V(G)$ is a separator if there is a partition $V=A\cup B\cup S$ such that $|A|,|B|\le 2n/3$ and there is no edge of $G$ between $A$ and $B$.
If $G$ is $k$-vertex connected, then for any separator $S$, $|S|\ge k$. But what about the other way around, if any separator $S$ satisfying $|S|\ge t$, what can we say about the vertex-connectivity $\lambda$? Is $\lambda$ a function in $t$? (I don't quite understand the role of $2n/3$ in the definition of a separator.)
