Color fixation and color identity in 4-chromatic graphs

2014/05/06 by Asbjørn Brændeland, Brændeland, Asbjørn
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM

paper · pdf · doi:10.48550/arxiv.1405.1323

6 pages, 7 figures

arxiv created 2014/05/06 · arxiv updated 2018/04/13

Abstract

I argue that there is no 4-chromatic planar graph with a joinable pair of color identical vertices, i.e., given a 4-chromatic planar graph G and a pair of vertices u, v in G, if the color of u equals the color of v in every 4-coloring of G, then there is no planar supergraph of G where u and v are adjacent. This is equivalent to the Four Color Theorem. (My argument is a variation of my argument in arXiv:1402.7368)

Citations

• Color identical pairs in 4-chromatic graphs

Related

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