Arc-disjoint in-trees in directed graphs

Naoyuki Kamiyama, Naoki Katoh, Atsushi Takizawa

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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 languageEnglish
Pages (from-to)197-214
Number of pages18
Issue number2
Publication statusPublished - Mar 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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