User blog comment:Hyp cos/SCG(n) and some related/@comment-1605058-20140811055544

What you are trying to say at the endof last section is probably that the graphs are outerplanar - we don't have three cycles which are pairwise fused and we also don't have a pair of cycles sharing multiple edges (you do not mention the latter restriction at all, while it's crucial to disallow graphs like \(K_{2,3}\)).