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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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b92057@yahoo.com

Posts: 1,187
Registered: 4/18/05
Re: A Simple Proof of The Four Color Theorem
Posted: Jul 3, 2013 2:22 AM
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On Tuesday, July 2, 2013 3:23:46 AM UTC-7, 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
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> >without worrying about the problem of "tangled chains"? Would
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> >that be sufficient for a proof?
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>
>
> 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. Heawood
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> identifies a specific planar graph which, if one follows Kempe's
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> coloring strategy, then two adjacent vertices will be forced to
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> have the same color. The result is to show that Kempe's proof is
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> invalid as a proof of 4-colorability for planar graphs.
>
>
>
> However, Heawood's graph _is_ a planar graph, hence it _can_ be
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> 4-colored (and probably easily so). So if you show a 4-coloring
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> of Heawood's graph, that reveals nothing we don't already know.
>
>
>
> quasi





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