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Topic: A Simple Proof of The Four Color Theorem
Replies: 10   Last Post: Jul 3, 2013 6:36 PM

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quasi

Posts: 10,315
Registered: 7/15/05
Re: A Simple Proof of The Four Color Theorem
Posted: Jul 2, 2013 6:49 AM
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quasi wrote:
>bill wrote:
>>
>>Kempe's method was accepted as proof of the FCT until
>>Heawood created his counter-example.
>>
>>Suppose that there was a simple way to 4-color Heawood's graph
>>without worrying about the problem of "tangled chains"? Would
>>that be sufficient for a proof?

>
>No.
>
>Heawood's graph is a counterexample to Kempe's proposed coloring
>strategy.
>
>According to Kempe's claimed proof, Heawood's graph can be
>4-colored by a specific strategy used in the proof.


The above line should read:

According to Kempe's claimed proof, _any_ planar graph can be
4-colored by a specific strategy used in the proof.

>Heawood identifies a specific planar graph which, if one follows
>Kempe's coloring strategy, then two adjacent vertices will be
>forced to have the same color. The result is to show that Kempe's
>proof is invalid as a proof of 4-colorability for planar graphs.
>
>However, Heawood's graph _is_ a planar graph, hence it _can_ be
>4-colored (and probably easily so). So if you show a 4-coloring
>of Heawood's graph, that reveals nothing we don't already know.


quasi



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