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Written by Vince Vatter on 2024-09-20 at 17:41

@zwol Assume there was a counterexample triangulation T that cannot be 4-colored. Then all the triangulations that contain T cannot be 4-colored either. By Theorem A, almost all triangulations contain T. So, if a positive proportion of all triangulations can be 4-colored, that means it cannot be the case that there is even a single triangulation that cannot be 4-colored.

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