The Four Color Theorem -- A New Simple Proof by Induction

2017/01/11 by Kamalappan, V. Vilfred
#05C10 #05C15 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1701.03511

Abstract

In 1976, Appel and Haken achieved a major break through by proving 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, Robertson, Sanders, Seymour and Thomas reproved the 4CT with less need for computer verification. In this paper, we present a simple proof to the 4CT based on mathematical induction and contraction. We consider, in our proof, possible colorings of a minimum degree vertex, its adjacent vertices and adjacent vertices of these adjacent vertices of simple planar graphs.

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