# The complexity of two graph orientation problems

Eggemann, N. and Noble, Steven
(2012)
The complexity of two graph orientation problems.
*Discrete Applied Mathematics* 160
(4-5),
pp. 513-517.
ISSN 0166-218X.

## Abstract

We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. Our main result is that for each positive integer , there is a linear-time algorithm that decides for a planar graph whether there is an orientation for which the diameter is at most . We also extend this result from planar graphs to any minor-closed family not containing all apex graphs. In contrast, it is known to be NP-complete to decide whether a graph has an orientation such that the sum of all the shortest path lengths is at most an integer specified in the input. We give a simpler proof of this result.

## Metadata

Item Type: | Article |
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School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Administrator |

Date Deposited: | 06 Jan 2023 14:22 |

Last Modified: | 09 Aug 2023 12:54 |

URI: | https://eprints.bbk.ac.uk/id/eprint/50373 |

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