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

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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.

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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

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Four color theorem: sage and multiple edges


Implementing, using Sagemath, the algorithm of Kempe reduction and the half Kempe chain color swithing (for Tait coloring), I need to avoid multiple edges and loops … OR I’ll not be able to use functions that need embedding, as for … Continue reading

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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

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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

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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

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