User blog comment:Hyp cos/SCG(n) and some related/@comment-36527-20140808162540/@comment-1605058-20140808165127

We can use this correspondence, by coding rooted ordered trees into subcubic graphs with no fused cycles, showing that "best possible" way of giving levels to graphs will make this type of graphs have order type SVO.

We can do it other way around too - by "rooting" such graphs in proper way we can embed them to rooted trees, showing that they don't have order type above SVO. This shows, non-rigorously, that triple edge in fact must have level SVO.