Cut-Vertex divides Graph into Two or More Components

Theorem
Let $G$ be a graph.

Let $v$ be a cut-vertex of $G$.

Then the vertex deletion $G - v$ contains $2$ or more components.

Proof
By definition of cut-vertex, $G - v$ contains at least $2$ components.

That it can contain more components than $2$ is best proved by illustration:


 * BigCutVertex.png