User blog comment:Wythagoras/Extension of SCG/@comment-1605058-20130813135100/@comment-1605058-20130814121647

Deedlit, I think there is a mistake in your sequence at the point where you get to trees. Please note that if you have subcubic trees with two valence 3 "nodes" we have K1,4 as a minor: we can simply cut and topologically contract edges to reach what I denoted G6 and then single edge contraction gives K1,4. First few graphs can be solid basis for my method, but one can show that G8 would be minor of G15 or some later graph.