User blog comment:Hyp cos/tree function and TREE(3)/@comment-5150073-20140624084600/@comment-5529393-20140625070810

@Hyp Cos: Actually, the "homeomorphic embedding" means similar things for both trees and subcubic graphs. (Only difference is that the trees are rooted, so the embedding must respect that.)  The term that is frequently used for SCG(n) is "topological minor", but that means the same thing as "homeomorphic embedding". But for subcubic graphs, "topological minor" and "minor" actually turn out to be the same thing! There's a nice proof of this on the net somewhere.

@Ikosarakt1: Hyp Cos's definition of "minor" seems to be the standard definition. His definition of "homeomorphic embedding" isn't the one Friedman uses, but as far as I can see it is equivalent.