@VinceVatter I don't quite follow the argument why Richmond–Robinson–Wormald Theorem A implies 4CT; it seems like there could still be a family of exceptions to 4CT as long as they are meagre relative to the set of all triangulations. Or to put it another way, it seems like the strongest statement Theorem A could possibly imply is that almost all triangulations (in the same technical sense) can be 4-colored.
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