
Re: A Simple Proof of The Four Color Theorem
Posted:
Jul 3, 2013 2:22 AM


On Tuesday, July 2, 2013 3:23:46 AM UTC7, quasi wrote: > bill wrote: > > > > >Kempe's method was accepted as proof of the FCT until > > >Heawood created his counterexample. > > > > > >Suppose that there was a simple way to 4color 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 4colored 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 4colorability for planar graphs. > > > > However, Heawood's graph _is_ a planar graph, hence it _can_ be > > 4colored (and probably easily so). So if you show a 4coloring > > of Heawood's graph, that reveals nothing we don't already know. > > > > quasi

