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# Tag Archives: Kempe chain

## Four color theorem: Infinite switches are not enough – Rectangular maps :-(

I transformed the really bad case into a rectangular map to play with the Java program and Kempe random switches. Here is the graph with the two edges to connect: The two edges marked with the X, have to be … Continue reading

## Four color theorem: Infinite switches are not enough :-( :-(

A new edge 12-7 that connects the edges 6-10 and 32-15. With this case seems that infinite random switches throughout the entire graph do not solve the impasse, which is really really really bad.

## Four color theorem: one switch is not enough :-(

Experimenting with the Python program, I have found that if you have an F5 impasse, a single switch may not be enough to solve the impasse. It means: counterexample found. This is a bad news, since I believed that a … Continue reading

## Four color theorem: down to a single case!

This post follows directly the previous one. I’m down to a single case to prove (pag. 3). I think I should move to Java coding, implementing the entire algorithm: map reduction (removing edges), color reduced map, restore of edges one at a … Continue reading

Posted in math
Tagged four color theorem, Graph theory, Kempe, Kempe chain, tait, Tait coloring
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## Four color theorem: experimenting impasses (as in life)

I still think a solution may be found in Kempe chain color swapping … for maps without F2, F3 and F4 faces (or even without this restriction). Or at least I want to try. How you can solve the impasses … Continue reading

Posted in math
Tagged 3-edge coloring, 4ct, coloring maps, four color problem, Kempe chain, Tait coloring
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## Four color theorem: Cahit spiral chains and Tait coloring

I was experimenting impasses and I found this about spiral chains: Consider all possible maps less than or equal to 18 faces (including the ocean) Do not consider duplicates (isomophic maps) There is still a very large number of possible … Continue reading

Posted in math
Tagged 3-edge coloring, four color theorem, Kempe chain, Tait coloring
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