In article <09-05-014@comp.compilers>,   
   Stephen Horne   wrote:   
      
   >BTW - am I correct in believing that a graph that can be coloured   
   >using four or fewer colours can always be drawn (in 2D) with no arcs   
   >crossing?   
      
   No.   
   K(3,3) (two triples of vertices, with each vertex in each triple having   
   edges to all three vertices in the other triple) can be colored with 2   
   colors, but doesn't have a planar embedding.   
      
      
   dave   
      
   --   
   Dave Vandervies                          dj3vande at eskimo dot com   
   Well, it's logically consistent and interesting. That appears to be   
   all mathematicians need.   
                            --James Riden in the scary devil monastery   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)