Color identical pairs in 4-chromatic graphs

2014/02/28 by Asbjørn Brændeland, Brændeland, Asbjørn · 2 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #math.GM

paper · pdf · doi:10.48550/arxiv.1402.7368

9 pages. A new lemma is introduced in order to correct an error in the proof of a lemma in the previous version

arxiv created 2014/03/25 · arxiv updated 2018/04/13

Abstract

I argue that, given vertices u and v in a 4-chromatic graph G, if the color of u equals the color of v in every 4-coloring of G then G has no planar supergraph where u and v are adjacent. This is equivalent to the Four Color Theorem.

Cited by

• Francis Guthrie's approach to The Four Color Problem
• Color fixation and color identity in 4-chromatic graphs

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• Mathematical Proofs of Two Conjectures: The Four Color Problem and The Uniquely 4-colorable Planar Graph
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• A Simple Proof of the Four-Color Theorem