On Equivalent Color Transform and Four Coloring Theorem

Wenhong Tian

On Equivalent Color Transform and Four Coloring Theorem

Data Structures and Algorithms 2016-10-07 v1

Authors: Wenhong Tian

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.

Keywords

graph coloring

Cite

@article{arxiv.1610.01865,
  title  = {On Equivalent Color Transform and Four Coloring Theorem},
  author = {Wenhong Tian},
  journal= {arXiv preprint arXiv:1610.01865},
  year   = {2016}
}

Comments

4 pages, 1 figure

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