Suppose someone came up with an algorithm that could take any snark and perform edge contraction to result in the Peterson graph. If an inspection of the algorithm reveals that it works as claimed, would the algorithm be sufficient to prove the 4CT?
4-Color Theorem – Proof by Contracting Snarks?
graph theorygraph-colorings
Best Answer
Yes, the 4-colour theorem is true if and only if every snark is non-planar (this is due to Tait).
Showing that a snark has a Petersen minor would be enough to show that it is non-planar.