User blog comment:Wythagoras/Minor(2)/@comment-1605058-20140213103921

Note that 3 dots is a minor of 3-path - we delete both edges, and we are done.

Proof that Minor(2)=SSCG(2):

Best we can do for 3. is a triangle - every other 3-vertex graph is minor of it. So we will not lose anything by starting with triangle (if it's a minor of some other graph, so is its every minor (graph minor relation ig transitive)). Now we have can only have a tree on 4 vertices - either a 4-path or K1,3. With 4-path we can't get very far, check yourself. With K1,3 we automatically limit ourselves to path forests, which have no degree 4 vertices. So we get no extra strength from using minor relation.