The oriented chromatic number χo(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 χo(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 χo(G) in terms of χα(G). An upper bound for χo(G) in terms of χα(G) was given by Raspaud and Sopena. We also give an upper bound for χo(G) in terms of the maximum degree of G. We shall show that this upper bound is not far from being optimal.
|Original language||English (US)|
|Number of pages||10|
|Journal||Journal of Graph Theory|
|State||Published - Apr 1997|
ASJC Scopus subject areas
- Geometry and Topology