### Blog Stats

- 15,456 hits

### Last visits

- 3-edge coloring 4 4 color theorem 4ct Alfred Bray Kempe algorithm Brendan McKay Cahit spiral chains color coloring coloring maps colour cubic graphs different edge embedding Euler four Four color four color music four color problem four colors suffice four color theorem Francis Guthrie Fullerene graph graph coloring Graph isomorphism graphs representations Graph theory Gunnar Brinkmann Hamilton homeomorphic impasse isomorphic graphs Java Kempe Kempe chain Kenneth Appel map new features oeis pencil and paper plantri problem proof proper colorings sage sagemath tait Tait coloring theorem tutte Wolfgang Haken
### Blogroll

### Comments

stefanutti on Quotes Todd Gibson on Quotes G.A. on Four color theorem: new i… Four color theorem:… on Four color theorem: back to th… Question about 3-reg… on Four color theorem: simplified… G.A. on Abstract Four color theorem:… on Four color theorem: counterexa… stefanutti on Four color theorem: representa… Guy on Four color theorem: representa… Brian Gordon on Four color theorem: 3-edge col… ### Meta

# 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

## 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
Leave a comment

## 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

Posted in math
Tagged Alfred Bray Kempe, four color theorem, graph coloring, Tait coloring
Leave a comment

## 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
1 Comment