Color identical pairs in 4-chromatic graphs

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.

arXiv comment9 pages. A new lemma is introduced in order to correct an error in the proof of a lemma in the previous version

Cited by in corpus (2)

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