A note on two conjectures that strengthen the four colour theorem
Combinatorics
2017-11-09 v1
Abstract
There are two conjectures concerning planar graph colourings that are strengthenings of the four colour theorem. One concerns signed graph colouring and is proposed by M\'{a}\v{c}ajov\'{a}, Raspaud and \v{S}koviera. It asserts that every signed planar graph is -colourable. Another concerns list colouring and is proposed by K\"{u}ndgen and Ramamurthi which asserts that if is a -list assignment of a planar graph , then there is an -colouring of such that each colour class induces a bipartite graph. In this note we prove that the first conjecture implies the second one.
Cite
@article{arxiv.1711.02848,
title = {A note on two conjectures that strengthen the four colour theorem},
author = {Xuding Zhu},
journal= {arXiv preprint arXiv:1711.02848},
year = {2017}
}