Friedman's SSCG function

Friedman's SSCG function is a mathematical function defined by Harvey Friedman. It is defined by ${\displaystyle {\text{SSCG}}(k)}$ as the largest integer ${\displaystyle n}$ satisfying the following:

There is a sequence ${\displaystyle G_{1},\ldots ,G_{n}}$ of simple subcubic graphs such that each ${\displaystyle G_{i}}$ has at most ${\displaystyle i+k}$ vertices and for no ${\displaystyle i<j}$ is ${\displaystyle G_{i}}$ homeomorphically embeddable into ${\displaystyle G_{j}}$.

Later, Friedman defined the more general subcubic graphs ${\displaystyle {\text{SCG}}(k)}$.