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arXiv · 1701.03511

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

V. Vilfred Kamalappan
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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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V. Vilfred Kamalappan. 2017-01-11. The Four Color Theorem -- A New Simple Proof by Induction. https://arxiv.org/abs/1701.03511

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