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# Tag Archives: tait

## 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: 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

Posted in math
Tagged Alfred Bray Kempe, four color theorem, Graph theory, tait, Tait coloring
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## Four color theorem: 3-edge coloring, impasse and Kempe chain color swapping

It is known that for regular maps, “3-edge coloring” is equivalent to finding a proper “four coloring” of the faces of a map. This post is about coloring impasses, fallacious Kempe chain color swapping (not solving the impasse) and an hypothesis I’d … Continue reading

## Four color theorem: work in progress

😦 Too many more things to do and little time: Filter out duplicates. I finally found a java library to efficiently filter out all isomorphic graphs. It is a library part if the sspace project. Using it I will be able … Continue reading

Posted in math
Tagged 4ct, Cahit spiral chains, coloring maps, four color theorem, Graph theory, tait, Tait coloring
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## Four color theorem: Tait edge coloring video

And here is the video that shows how to get a Tait colored map (graph) from a rectangular map.

## Four color theorem: Tait edge coloring

From Wikipedia: “The four color theorem, on vertex coloring of planar graphs, is equivalent to the statement that every bridgeless 3-regular planar graph is of class one (Tait 1880). This statement is now known to be true, due to the … Continue reading