
Re: A New Graph Coloring Conjecture.
Posted:
Jun 20, 2013 8:02 PM


On Wednesday, June 19, 2013 9:25:28 PM UTC7, quasi wrote: > bill wrote: > > > > > >Okay. > > > > > >Finite planar graphs are 4C because they cannot > > >contain subgraphs isomorphic to K5! > > > > > >My thinking is thus. In any K4 subgraph one vertex is > > >unavailable. Therefore, there is no way to force any set of > > >4 vertices to have four different colors. Tangled chains are > > >not due to the congiguration of the graph but result from a > > >fortuitous coloring. Plus, if two chains are tangled; there > > >will be two that are not tangled. > > > > > >If there are no forceable sets of four vertices, the graph > > >must be 4 colorable. > > > > Except that I've already shown you a counterexample. > I suspect that your example is nonplanar. > > quasi

