Oriented colourings of graphs with maximum degree three and four

@article{Duffy2018OrientedCO,
  title={Oriented colourings of graphs with maximum degree three and four},
  author={Christopher Duffy and Gary MacGillivray and {\'E}ric Sopena},
  journal={ArXiv},
  year={2018},
  volume={abs/1812.05510}
}
We show that any orientation of a graph with maximum degree three has an oriented 9-colouring, and that any orientation of a graph with maximum degree four has an oriented 69-colouring. These results improve the best known upper bounds of 11 and 80, respectively. 
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