\begin{definition}[Definition:K-Connected]
Let $G = \struct {V, E}$ be a graph.
Let $k \in \Z_{>0}$.
Then $G$ is '''$k$-connected''' {{iff}}:
: $\card V > k$
: $G$ is connected
: $G$ has no vertex cut $W$ with $\card W < k$
Informally:
: $G$ is connected and has more than $k$ vertices
: There is no vertex cut of $G$ containing less than $k$ vertices.
\end{definition}