The Four Color Theorem - A New Proof by Induction
V. Vilfred Kamalappan · arXiv (Cornell University) · 2017
In 1976 Appel and Haken achieved a major break through by thoroughly establishing the Four Color Theorem (4CT). Their proof is based on studying a large number of cases for which a computer-assisted search for hours is required. In 1997 the 4CT was reproved with less need for computer verification by Robertson, Sanders, Seymour and Thomas. In 2000 Ashay Dharwadkar gave an algebraic proof to the 4CT involving Steiner Systems, Eilenberg Modules, Hall Matching and Riemann Surfaces. In this paper, we give a simple proof to the $4CT$. The proof is based on the Principle of Mathematical Induction, contraction, and possible colorings of a minimum degree vertex, its adjacent vertices, and adjacent vertices of these adjacent vertices.