Four color theorem: Cahit spiral chains and Tait coloring


I was experimenting impasses and I found this about spiral chains:

  • Consider all possible maps less than or equal to 18 faces (including the ocean)
  • Do not consider duplicates (isomophic maps)
  • There is still a very large number of possible such maps
  • Remove all maps that have faces with 2, 3, 4 edges
  • The number of maps reduces to 22 maps only
  • All these 22 maps have only one spiral chain
  • To get the Tait coloring, required me only one Kempe chain color swapping per map
  • Actually I complitely colored the spiral (the backbone) with two colors and then I finished the other edges and at the end I worked on impasses
  • Next, I’ll try the algorithm described here:
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About stefanutti

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