## Abstract

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_{α}(G). An upper bound for χ_{o}(G) in terms of χ_{α}(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.

Original language | English (US) |
---|---|

Pages (from-to) | 331-340 |

Number of pages | 10 |

Journal | Journal of Graph Theory |

Volume | 24 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1997 |

Externally published | Yes |

## ASJC Scopus subject areas

- Geometry and Topology