A Note on Colourings of Connected Oriented Cubic Graphs
Discrete Mathematics
2020-06-17 v3 Combinatorics
Abstract
In this note we show every orientation of a connected cubic graph admits an oriented 8-colouring. This lowers the best-known upper bound for the chromatic number of the family of orientations of connected cubic graphs. We further show that every such oriented graph admits a 2-dipath 7-colouring. These results imply that either the chromatic number for the family of oriented connected cubic graphs equals the 2-dipath chromatic number or the long-standing conjecture of Sopena [Journal of Graph Theory 25:191-205 1997] regarding the chromatic number of orientations of connected cubic graphs is false.
Keywords
Cite
@article{arxiv.1908.02883,
title = {A Note on Colourings of Connected Oriented Cubic Graphs},
author = {Christopher Duffy},
journal= {arXiv preprint arXiv:1908.02883},
year = {2020}
}