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
  • These maps, as found by Kempe back in 1879, can be not considered
    • See http://en.wikipedia.org/wiki/Four_color_theorem:
      • “Kempe also showed correctly that G can have no vertex of degree 4″
• 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:
  • www.academia.edu