User blog comment:Wythagoras/Graphs/@comment-1605058-20140913123957

About your improvement on SCG SSCG relationship, note that if original sequence first two graphs have n, n+1 vertices, then after reduction they might have 3n, 3n+3, which is incorrect.

I don't really see how your reduction works - suppose we want to change K4 using it (it's simple, but as far as I get it your reduction is very general and allows that). Then we would have 4 pairwise fused triangles change to pairwise fused pentagons. On the other hand, we have multiple length 4 cycles in K4, which are supposed to go into hexagons. They aren't visible in planar drawing, but they are there. Also, you didn't prove sharp inequality - there is a possibility of equality, unless you prove otherwise.