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# Tag Archives: 4ct

## 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

Posted in math
Tagged 3-edge coloring, 4ct, coloring maps, four color problem, Kempe chain, Tait coloring
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## Four color theorem: counterexample to the hypothesis I was verifying :-(

Bad news … to me! This example it is a counterexample to the hypothesis I was trying to verify! Map signature: 1b+, 4b+, 6b+, 15b+, 7b-, 14b-, 8b-, 12b-, 13b-, 11b-, 9b-, 8e-, 7e-, 5b-, 6e-, 9e-, 10b-, 5e-, 4e-, 3b-, 10e-, 11e-, 12e-, 3e-, 2b-, … Continue reading

## Four color theorem: Tait edge coloring and Kempe switch

In this new version of the software you can manually color the edges of a map with three colors (RGB) and apply Kempe coloring switch on a Kempe edge chain (path or loop) (http://en.wikipedia.org/wiki/Kempe_chain).

Posted in math
Tagged 4ct, Cahit spiral chains, four color theorem, Kempe chain, Tait coloring
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## Four color theorem: simplified maps and fullerenes (answer)

After having posted the question on mathoverflow, the answer arrived in a blink of an eye. Here is the answer from Gordon Royle: Use Gunnar Brinkmann (University of Ghent) and Brendan McKay (Australian National University)’s program “plantri” … You will … Continue reading

Posted in math
Tagged 4ct, Brendan McKay, four color theorem, Fullerene, Gunnar Brinkmann, oeis
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## Four color theorem: simplified maps and fullerenes

Analyzing all 3-regular graphs that have only faces with 5 edges or more (simplified), I empirically found (using a computer program) that many hypothetically possible graphs, that by Euler’s identity may exist (), do not actually exist. Using a VF2 algorithm to filter out … 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: Cahit spiral chains (step two)

Now the application is able to find all spiral chains of a graph. I still need to: Implement the Cahit coloring algorithm using the spiral chains Add some additional features to the Java application Modify the settings to color the … Continue reading

Posted in Uncategorized
Tagged 4ct, Cahit spiral chains, coloring maps, Four color, Tait coloring
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