## Abstract

A graph has a unilateral orientation if its edges can be oriented such that for every two vertices *u* and *v* there exists either a path from *u* to *v* or a path from *v* to *u*. If *G* is a graph with a unilateral orientation, then the *forced unilateral orientation number* of *G* is defined to be the minimum cardinality of a subset of the set of edges for which there is an assignment of directions that has a unique extension to a unilateral orientation of *G*. This paper gives a general lower bound for the forced unilateral orientation number and shows that the unilateral orientation number of a graph of size *m*, order *n*, and having edge connectivity 1 is equal to *m* - *n* + 2. A few other related problems are discussed.

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

Pages (from-to) | 171-183 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 187 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 6 Jun 1998 |

Externally published | Yes |