I was asked to compute the outerplanarity of (n x m)-grid graph where a given hint was "a grid doesn't need to be drawn as a grid. There are also other ways to draw it!".
So, I tried to redraw a 4x5 grid by bringing a square from the center to the outside and the outside vertices to the inside. It looks strange but I couldn't imagine a different way of drawing it. However, as I understood, k-outerplanarity means: in k-1 steps of deleting the outer vertices I get a outerplanar graph, i.e. all vertices left are incident to the outer plane.
For my 4x5 grid I think k should be 2 as after deleting the outer vertices once I have a outerplanar graph already. Whereas my redrawing looks like k=3. Can anyone see what I have been probably overlooking? Or can help me with the hint?