it's a beginning of my proof on four color theorem. I'm trying to prove the degrees of every node on my five color map.I cannot understand what you are trying to prove. Please state your theorem upfront before describing those transformation.
Also, are you considering only planar maps (which seems to be the case in every complete drawing) ?
With this kind of size you might not be too many volunteers to read the proof. Have you looked at the existing proofs?it's a beginning of my proof on four color theorem.
If you look up the definition of complete graph you'll find it means something different. It seems that at least in same places the term "maximal planar graph" is used for your concept.A "complete map" is a map (or a graph) could not add more connections (lines) between nodes, or the lines will intersect each other.
Thank you for your correcting, maximal map is what I mean, or "triangular graph"or "triangulated graph".If you look up the definition of complete graph you'll find it means something different. It seems that at least in same places the term "maximal planar graph" is used for your concept.
The beginning is heavily based on Kempe Chain, I want it to be verified, because I don't want to make a fault too early like a crank.With this kind of size you might not be too many volunteers to read the proof. Have you looked at the existing proofs?
I haven't gotten to this stage. I simply don't know enough on the subject to be effective in this area.Which part, section, phrase or paragraph confusing you?