## Four color theorem: back to the basics

Finally I bought two books about the four color theorem: “Four Colors Suffice: How the Map Problem Was Solved” by Robin Wilson e Ian Stewart; and the “The Four-Color Theorem: History, Topological Foundations, and Idea of Proof” by Rudolf Fritsch and Gerda Fritsch.

I’am in the middle of reading the first one and I want to go back to the basics and use the method used by Kempe when he belived he had solved the problem.

With these differences: Instead of shrinking down to a point the faces with less than 6 edges, I will remove from these faces one edge at a time, from F2, F3. From the F4 faces I will remove two opposite edges. And from F5 or F5-F5 or F5-F6 (unavoidable sets) I will try to remove two or more edges. This way, after having reduced the map to two single faces (including the ocean), I will restore the edges in reverse order, this way always dealing with 3-regular planar graphs, and instead of applying Kempe’s chain color switching to the faces, I will consider also Tait coloring of the edges and Kempe’s chain color switching to the egdes.

Follow the arrow to visualize the steps: