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- 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
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Tag Archives: 4ct
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
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
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).
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
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
😦 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
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