## Abstract

Given a directed graph D = (V,A) with a set of d specified vertices S = {s _{1}, s _{d} } V and a function f: S → where denotes the set of natural numbers, we present a necessary and sufficient condition such that there exist ∑ _{i=1} ^{d} f(s _{i} ) arc-disjoint in-trees denoted by T _{i,1},T _{i,2}, T i,f(s0 ) for every i = 1, d such that T _{i,1}, T i,f (s0 ) are rooted at s _{i} and each T _{i,j} spans the vertices from which s _{i} is reachable. This generalizes the result of Edmonds [2], i.e., the necessary and sufficient condition that for a directed graph D=(V,A) with a specified vertex s V, there are k arc-disjoint in-trees rooted at s each of which spans V. Furthermore, we extend another characterization of packing in-trees of Edmonds [1] to the one in our case.

Original language | English |
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Pages (from-to) | 197-214 |

Number of pages | 18 |

Journal | Combinatorica |

Volume | 29 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2009 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Computational Mathematics