- 15,662 hits
- 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
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…
Some rights reserved. Read here.
Author Archives: stefanutti
For the decomposition of a graph representing a map, I’m trying to use different algorithms to select the edge to remove. The question is: When you have multiple valid choices, which is the best edge to select … if any? Some basic … Continue reading
This is what I want to try: Select an F2, F3 or F4 preferably when it is near an F5 and remove the edge that joins the two faces Analyse also the balance of the Euler’s identity when removing edges, to … Continue reading
The algorithm I use to color graphs works pretty well … BUT: Sometimes (very rarely) it gets into an infinite loop where also random Kempe color switches (around the entire graph) do NOT work. The good is, if I reprocess … Continue reading
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
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.
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