### Abstract

A 2-assignment on a graph G= (V,E) is a collection of pairs L(v) of allowed colors specified for all vertices v ∈ V. The graph G (with at least one edge) .is said to have oriented choice number 2 if it admits an orientation which satisfies the following property: For every 2-assignment there exists a choice c(v) ∈L(v) for all v ∈V such that (i) if c(v)=c(w), then vW ∈ E, and (ii) for every ordered pair (a,b) of colors, if some edge oriented from color a to color b occurs, then no edge is oriented from color b to color a. In this paper we characterize the following subclasses of graphs of oriented choice number 2: matchings; connected graphs; graphs containing at least one cycle. In particular, the first result (which implies that the matching with 11 edges has oriented choice number 2) proves a conjecture of Sali and Simonyi

Original language | English |
---|---|

Pages (from-to) | 217-229 |

Number of pages | 13 |

Journal | Journal of Graph Theory |

Volume | 36 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2001 |

### Keywords

- Directed graphs
- List colorings
- Oriented colorings

### ASJC Scopus subject areas

- Geometry and Topology

## Fingerprint Dive into the research topics of 'Oriented list colorings of graphs'. Together they form a unique fingerprint.

## Cite this

*Journal of Graph Theory*,

*36*(4), 217-229. https://doi.org/10.1002/1097-0118(200104)36:4<217::AID-JGT1007>3.0.CO;2-1