User blog comment:Hyp cos/SCG(n) and some related/@comment-1605058-20140814064902/@comment-11227630-20140814162018

4th bullet: The graph G itself has cycle level a - the minimum of all the planar drawings.

5th bullet: A stick is a CLG of two fusing cycles no matter what they share. e.g. the level $$\vartheta(\Omega^\omega)$$ graph and the level $$\vartheta(\varepsilon_{\Omega+1})$$ graph. The reason is, in map f, a and b are fused (no matter what they share) then f(a) and f(b) are linked by one edge.

6th bullet: Outerplanar graphs are graphs that have no planar drawing, I think. Or what do you think about "outerplanar graph"?

7th bullet: Can you tell me more about the "tree-width"?