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Tag Archives: 4ct
4CT and loops, cycles, circuits, chains, paths
I realized that for some posts I may have used “Kempe loops” and “Kempe cycles” to describe closed “Kempe chains”, that in other words form closed paths (cycles). I think it would have been better always to use “Kempe cycles”. … Continue reading
Non-Hamiltonian 3-regular planar graphs, Tait coloring and Kempe cycles … what else ;-)
Non Hamiltonian 3-regular planar graphs, Tait coloring and Kempe loops. Continue reading
Tait coloring and the four color theorem: personal Q&A
Connections between the Tait coloring of a map and the Four Color Theorem. Continue reading
Posted in math
Tagged 4ct, four color theorem, pencil and paper, proof, Tait coloring
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Generate planar graphs
A python program to fenerate planar graphs and save them as planar embedding Continue reading
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 blog 