On Equivalent Color Transform and Four Coloring Theorem

Wenhong Tian

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arXiv · 1610.01865

On Equivalent Color Transform and Four Coloring Theorem

Wenhong Tian

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Abstract

In this paper, we apply an equivalent color transform (ECT) for a minimal $k$-coloring of any graph $G$. It contracts each color class of the graph to a single vertex and produces a complete graph $K_k$ for $G$ by removing redundant edges between any two vertices. Based on ECT, a simple proof for four color theorem for planar graph is then proposed.

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Wenhong Tian. 2016-10-06. On Equivalent Color Transform and Four Coloring Theorem. https://arxiv.org/abs/1610.01865

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