Colouring Graphs

[Jim Nastos]

On Mon, 3 Feb 2003, Jon Perry wrote:

> If what you are saying is that the problem can be expanded, and the results
> are the same, I do not believe this to be true, at least not obviously so.

  I don't know what you mean by "expanding" the problem, but what I'm 
saying that your proposed colouring is not interesting enough to study 
because it is easily transformed into a kind of colouring problem that has 
been studied for hundreds of years already.
  And this is fairly obvious; as obvious that your conjecture on
http://www.users.globalnet.co.uk/~perry/maths/longestpath/longestpath.htm
  can be answered in the negative, or as obvious that your partial 
solution to the Hamiltonian problem on
http://www.users.globalnet.co.uk/~perry/maths/hamiltoniancycles/hamiltoniancycles.htm
is equivalent to saying that a graph with n vertices and n edges is either 
disconnected or a cycle, and as obvious that your 5 line proof of the 
4-colour theorem here:
http://www.users.globalnet.co.uk/~perry/maths/fourcolour/fourcolour.htm
is insufficient.

Jim