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Originally Posted by hhEb09'1
As I said, it may not make a difference in the proof, but it is not true that all three have to touch the other two, even if they are all connected.
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But we already know that we may as well only consider maximal planar graphs, because if they are four-colorable, then trivially so are non-maximal ones. I'm having difficulty seeing how non-maximal ones could be crucial to any proof. But then you could say that we also know from Kempe that we might as well start with a vertex with five edges, and assume that the rest of the map is four-colorable, but this is
Maddad's proof, so we should stay open minded as you say, and see where he's going. Let's hope this one doesn't take 10 years to disprove
