Definition:K-Connected

Definition

Let $G = \struct {V, E}$ be a graph.

Let $k \in \Z_{>0}$.

Then $G$ is $k$-connected if and only if:

$\card V > k$

$G$ 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.

Also see

• Definition:Connectivity

• Results about connectedness in the context of graph theory can be found here.

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