Oriented coloring of graphs with low maximum degree
Abstract
Duffy et al. [C. Duffy, G. MacGillivray, and \'E. Sopena, Oriented colourings of graphs with maximum degree three and four, Discrete Mathematics, 342(4), p. 959--974, 2019] recently considered the oriented chromatic number of connected oriented graphs with maximum degree and , proving it is at most and , respectively. In this paper, we improve these results by showing that the oriented chromatic number of non-necessarily connected oriented graphs with maximum degree (resp. ) is at most (resp. ). The bound of actually follows from a general result which determines properties of a target graph to be universal for graphs of bounded maximum degree. This generalization also allows us to get the upper bound of (resp. , ) for the oriented chromatic number of graphs with maximum degree (resp. , ).
Cite
@article{arxiv.1905.12484,
title = {Oriented coloring of graphs with low maximum degree},
author = {Pascal Ochem and Alexandre Pinlou},
journal= {arXiv preprint arXiv:1905.12484},
year = {2019}
}