TY - JOUR

T1 - Independent arborescences in directed graphs

AU - Frank, András

AU - Fujishige, Satoru

AU - Kamiyama, Naoyuki

AU - Katoh, Naoki

N1 - Funding Information:
The second, third and fourth author’s work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan .
Funding Information:
First author received a grant (no. CK 80124 ) from the National Development Agency of Hungary , based on a source from the Research and Technology Innovation Fund. Part of research was done while he visited the Research Institute for Mathematical Sciences, Kyoto University, 2008.

PY - 2013

Y1 - 2013

N2 - As a vertex-disjoint analogue of Edmonds' arc-disjoint arborescences theorem, it was conjectured that given a directed graph D with a specified vertex r, there are k spanning arborescences rooted at r such that for every vertex v of D the k directed walks from r to v in these arborescences are internally vertex-disjoint if and only if for every vertex v of D there are k internally vertex-disjoint directed walks from r to v. Whitty (1987) [10] affirmatively settled this conjecture for k≤2, and Huck (1995) [6] constructed counterexamples for k≥3, and Huck (1999) [7] proved that the conjecture is true for every k when D is acyclic. In this paper, we generalize these results by using the concept of "convexity" which is introduced by Fujishige (2010) [4].

AB - As a vertex-disjoint analogue of Edmonds' arc-disjoint arborescences theorem, it was conjectured that given a directed graph D with a specified vertex r, there are k spanning arborescences rooted at r such that for every vertex v of D the k directed walks from r to v in these arborescences are internally vertex-disjoint if and only if for every vertex v of D there are k internally vertex-disjoint directed walks from r to v. Whitty (1987) [10] affirmatively settled this conjecture for k≤2, and Huck (1995) [6] constructed counterexamples for k≥3, and Huck (1999) [7] proved that the conjecture is true for every k when D is acyclic. In this paper, we generalize these results by using the concept of "convexity" which is introduced by Fujishige (2010) [4].

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U2 - 10.1016/j.disc.2012.11.006

DO - 10.1016/j.disc.2012.11.006

M3 - Article

AN - SCOPUS:84870696714

VL - 313

SP - 453

EP - 459

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 4

ER -