Comment by Certhas

CH as I understand it has nothing to do with this. As an example that illustrates why, consider the simple infinite coloring discussed in the article that uses the axiom of choice. You could not write an algorithm that actually performs this coloring (because Axiom of Choice, and because it requires uncountably many actions). CH says that the statement "all such graphs can be colored" can be computed (in finitely many steps) by a program from the axioms. Even though the colorings can-not be done by a computation.

What CH does not allow you to do is turn an existence proof (a coloring exists) into a constructive proof (a means to actually construct such a coloring). In fact, this is generally not true. Mathematical statements correspond to computations in a much more subtle and indirect way than that.

Honestly, I get the impression that you have a very superficial understanding of the topics at hand, but I am far from an expert myself. If you really know a way to see this as an instance of CH I would be very intrigued to learn about it.