My proof on 5 color map

[lrerpqu]

 

[lrerpqu]

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Can somebody write a comment for it?

 

[blamocur]

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) ?

 

[lrerpqu]

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) ?

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.
A "complete map" is a map (or a graph) could not add more connections (lines) between nodes, or the lines will intersect each other. I learn this word from a computer programming book written in my language，but I don't know the real name of it in English.
Isn't planar maps can be converted to "line node map"?

 

[blamocur]

it's a beginning of my proof on four color theorem.

With this kind of size you might not be too many volunteers to read the proof. Have you looked at the existing proofs?

A "complete map" is a map (or a graph) could not add more connections (lines) between nodes, or the lines will intersect each other.

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.

 

[lrerpqu]

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.

Thank you for your correcting, maximal map is what I mean, or "triangular graph"or "triangulated graph".

With this kind of size you might not be too many volunteers to read the proof. Have you looked at the existing proofs?

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.
Which part, section, phrase or paragraph confusing you?

 

[blamocur]

Which part, section, phrase or paragraph confusing you?

I haven't gotten to this stage. I simply don't know enough on the subject to be effective in this area.