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Acyclic and oriented chromatic numbers of graphs

✍ Scribed by Kostochka, A. V.; Sopena, E.; Zhu, X.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 121 KB
Volume: 24
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199704)24:4<331::aid-jgt5>3.0.co;2-p

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✦ Synopsis

The oriented chromatic number χ o ( G) of an oriented graph G = (V, A) is the minimum number of vertices in an oriented graph H for which there exists a homomorphism of G to H. The oriented chromatic number χ o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the orientations of G. This paper discusses the relations between the oriented chromatic number and the acyclic chromatic number and some other parameters of a graph. We shall give a lower bound for χ o (G) in terms of χ a (G). An upper bound for χ o (G)in terms of χ a (G) was given by Raspaud and Sopena. We also give an upper bound for χ o (G) in terms of the maximum degree of G. We shall show that this upper bound is not far from being optimal.

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