A snark is a connected, bridgeless and cubic. The snark is 4 (E)colorable,
But is it planar?
The snark theorem says that the 4CT is equivalent to saying that NO snark is planar!
Cubics have an even number of vertices, 1,5*v edges and 0.5*n-2 faces.
A cubic with a hamiltonian is 3 (E) colorable
If the cubic is 3 EC, then it is 4 FC. If the cubic is not 3 EC and
therefore cannot be 4 FC. If the cubic is not 4 FC then it must
be non-planar with a K5 minor.
But how do you get a K5 minor without 5 vertices of degree 5?
Perhaps by contraction? No!
The snark is K3,3 non-planar, which means that it is 3 VC
Let's examine the premise that "The existence of a planar snark negates the 4CT.
b