Author Archives: stefanutti

Four color theorem: about edges selection


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

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Four color theorem: new ideas


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

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Four color theorem: what next?


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

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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

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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.

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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

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Four color theorem: A fast algorithm


I have implemented an algorithm that goes really fast coloring the edges of a planar graph. See this video and then try it youself! Note about the Python program: To try the Python program you need to have Sage. Follow … Continue reading

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