Subcubic graph number

Define the function SCG(k) as the length of the longest sequence of subcubic graphs G1,...,Gn such that each Gi has at most i + k vertices and for no i < j is Gi homeomorphically embeddable into Gj. The value SCG(13), investigated by Harvey Friedman, is extremely large. Little is known about it except it is far larger than TREE(3).