A Most Simple, Non-Computer-Aided Proof Of The Four-Color Theorem

An alternative brief proof of the Four Color Theorem without using a computer is described. The proof is essentially similar to the brief proof very recently described by the author as a bird's-eye view, but is much more simple than that, and more importantly, differs from that in the way of vertex-reducing of complete triangulation graph. This new, most simple proof is much shorter than the recently described one, and both of these two proofs are far more easily understood than Appel and Haken's proof in 1977. These new findings of non-computer-aided proofs clearly tell us about what the essential portion of the enormous complexity of the Four Colour Theorem is.