quasi
Posts:
12,057
Registered:
7/15/05


Re: 4 colors problem
Posted:
Mar 5, 2014 3:38 PM


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 4color theorem.
The 4color theorem does _not_ guarantee that any partial 4coloring of a planar graph can be extended to a 4coloring 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 4color 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 4color 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

