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.