Tag Archives: Tait coloring

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: almost there?


Here there are some results that came out from the study of Kempe chains/cycles (of edges) in Tait coloring of a 3-regular planar graph. Next is shown an image with a summary of the ideas behind this approach. I didn’t have the time to … Continue reading

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Four color theorem: back to the basics


Finally I bought two books about the four color theorem: “Four Colors Suffice: How the Map Problem Was Solved” by Robin Wilson e Ian Stewart; and the “The Four-Color Theorem: History, Topological Foundations, and Idea of Proof” by Rudolf Fritsch and Gerda Fritsch. I’am in … Continue reading

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