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Topic: 4 colors problem
Replies: 86   Last Post: Mar 13, 2014 4:36 PM

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 quasi Posts: 12,067 Registered: 7/15/05
Re: 4 colors problem
Posted: Mar 5, 2014 4:42 PM

swtchwrds88 wrote:

>Partial coloring using a specific sequence of given 4 colors,

You still don't get it.

I'll try again ...

The 4-color theorem doesn't claim that every partial 4-coloring
of a planar graph can be completed to a full 4-coloring.

The claim of the theorem is that of _all_ possible valid
colorings, at least one of them uses at most 4 colors.

Thus, to show that a given planar graph is a counterexample to
the 4-color theorem, it's not sufficient to produce a partial
4-coloring which can't be completed to a full coloring.

You would have to show that _all_ possible valid colorings use
more than 4 colors, not just the one that you think makes sense.

If you get it -- fine, but I have no more time for this, so I'm

quasi

PS:

Google groups offers an option for automatically quoting
the prior message. Look for it.

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