Apollonian network and 4 coloring Is there a connection between the Apollonian network and the four-color theorem? Are there any attempts to prove this theorem using the Apollonian network?

As Wikipedia's article on Apollonian networks mentions, " _Birkhoff (1930) is an early paper that uses a dual form of Apollonian networks, the planar maps formed by repeatedly placing new regions at the vertices of simpler maps, as a class of examples of planar maps with few colorings._ " This refers to Birkhoff, On the number of ways of colouring a map.

More recently, Fowler proved in his PhD thesis Unique Coloring of Planar Graphs (1998) that every uniquely 4-colorable graph is an Apollonian network, and the Four Color theorem follows from this. Curiously, he does not cite Birkhoff's 1930 paper and does not use the name "Apollonian network". See Brændeland's Color fixation, color identity and the Four Color Theorem for a different take on Fowler's theorem.