Q:

Max-Cut not optimal solution example?

I currently learning about the Max-Cut problem, but i'm little bit confused about how the 2-approximation algorithm works. The algorithm is as follows:  

Start with an arbitrary partition
Find a vertex $u$ with more outgoing edges in its own side than to the other.
If such a $u$ exists, switch $u$ to the other side and goto Step 2.
Otherwise, end the procedure.

I can't find example of a graph that this algotihm doesn't return the optimal solution. can someone give me an example?

A:

I used an electronic computer to find this answer, a graph with 4 vertices:

The graph is given in green.  The blue cut is the optimum partition: $\{\{1, 3\}, \{2, 4\}\}$, with a cut size of 3.
The red cut, $\{\{1, 2\}, \{3, 4\}\}$ has no vertices that your algorithm would move, because they all have equal or more outgoing edges.

