Date: Mar 5, 2014 3:38 PM
Author: quasi
Subject: Re: 4 colors problem
swtchwrds88 wrote:

>

>So far there has not been a single point raised for any errors

>or omissions or faulty or incomplete logic in the way this

>conclusion was reached.

I haven't followed the thread in full, but my sense is that

you misunderstand the claim of the 4-color theorem.

The 4-color theorem does _not_ guarantee that any partial

4-coloring of a planar graph can be extended to a 4-coloring

of the full graph.

Rather, it asserts that for a planar graph there exists at

least one valid coloring using at most 4 colors.

Thus, to find a counterexample to the 4-color theorem, you

would have to produce a planar graph such that _all_ valid

coverings (not just one of your choosing) use more than

4 colors.

However, the very fact that the 4-color theorem is actually

a theorem (the logic of the proof has been extensively

analyzed and verified) guarantees that any attempt to produce

such a counterexample will fail.

quasi