### Abstract

Suppose that we are given a directed graph D = (V, A) with specified vertices r_{1}, r_{2} ∈ V. In this paper, we consider the problem of discerning the existence of a pair of arc-disjoint spanning in-arborescence rooted at r_{1} and out-arborescence rooted at r_{2}, and finding such arborescences if they exist. It is known (Bang-Jensen (1991) [1]) that this problem is NP-complete even if r_{1} = r_{2}. As a special case, it is only known (Bang-Jensen (1991) [1]) that this problem in a tournament can be solved in polynomial time. In this paper, we give a linear-time algorithm for this problem in a directed acyclic graph. We also consider an extension of our problem to the case where we have multiple roots for in-arborescences and out-arborescences, respectively.

Original language | English |
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Pages (from-to) | 1227-1231 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 109 |

Issue number | 23-24 |

DOIs | |

Publication status | Published - Nov 15 2009 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

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## Cite this

*Information Processing Letters*,

*109*(23-24), 1227-1231. https://doi.org/10.1016/j.ipl.2009.09.004