User blog comment:Wythagoras/Graphs/@comment-1605058-20140913123957/@comment-5529393-20140913223345

As I mentioned to LittlePeng9 on IRC, I believe the resolution is to subdivide every edge. (regular edges into two edges, loops into three)  We would need to prove that a correct sequence for SCG leads to a correct sequence for SSCG, but I believe that to be the case.

The inequality will have to go to SCG(n) < SSCG(3.5n + c), unless we optimize further. Perhaps we only subdivide edges that are part of cycles - that would be enough to lower it back to SCG(n) < SSCG(3n + 4).