[see also: case]
The possibility $A=\emptyset$ is not excluded.
The only possibility for $G$ not to be 1-1 is that there exists ......
The remaining possibility is that $v$ is labelled 2.
These two possibilities cannot arise simultaneously.
However, this still left open the possibility that the converse of Theorem 3 held for $m=3$.
The reader may wonder why we have apparently ignored the possibility of obtaining a better lower bound by considering ...... [Not: “the possibility to obtain”]
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