Tag Archives: Tait coloring

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Four color theorem: A fast algorithm – 2


https://4coloring.wordpress.com/2016/10/16/four-color-theorem-a-fast-algorithm These are the OLD and NEW (last column) execution times on my new laptop: 100 – 196 vertices, 294 edges = 0 seconds – 0 seconds 200 – 396 vertices, 594 edges = 1 seconds – 0 seconds 300 – 596 vertices, 894 edges = … Continue reading

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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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