One consequence of the three tree theorem is that the planar graphs have arboricity less or equal than 3. I heared this first from “Bard” the Google AI system. Since this bot had hallucinated in the same conversation terribly like claiming that the circular graph has arbitrary 1. Somehow, the bot had picked up an exercise one can find in the Bondy-Murty book which establishes this. September 4th: here is a draft of the paper.[PDF]

And here is the recording.