Color identical pairs in 4-chromatic graphs
General Mathematics
2018-04-13 v4
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.
Keywords
Cite
@article{arxiv.1402.7368,
title = {Color identical pairs in 4-chromatic graphs},
author = {Asbjørn Brændeland},
journal= {arXiv preprint arXiv:1402.7368},
year = {2018}
}
Comments
9 pages. A new lemma is introduced in order to correct an error in the proof of a lemma in the previous version