Commentary

COMMENTARY

After spending some fifty-five years in an awkward and fruitless search for a simple solution to the famous “Four Color Conjecture,” and after being intimidated by the counter-examples by Heawood and Errera, the thought came to me that perhaps researchers were concentrating on coloring the wrong region. I wondered what would happen if counter-examples could be re-colored in a way that would produce a new map that could be properly colored using Kempe’s method of color exchanges. To my surprise, I found that an exchange of colors in the R-X, or S-X chain in the above examples would produce a new map that could easily be properly colored using Kempe’s method. Thus my hope that my theorem should be called “Kempe’s Revenge” in that it restores the validity of his approach and provides the final step needed to complete a “pencil and paper” solution to the problem.

In a way, the “McCracken Theorem” turns out to be so simple “that a caveman could do it.” As Paul Harvey might say, “Now you know the rest of the story.”