A generalization of the 5-color theorem
Paul C. Kainen · Proceedings of the American Mathematical Society · 1974
We present a short topological proof of the 5 5 -color theorem using only the nonplanarity of K 6 {K_6} . As a bonus, we find that any graph which becomes planar upon the removal of 2 edges can be 5 5 -colored and that any graph which becomes planar when 5 edges are removed is 6 6 -colorable.