Subcubic graph number

SCG(13) is a large number used in Harvey Friedman's research.

SCG(k) is defined as 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.

Little is known about SCG(13) except it is far larger than TREE(3).