Abstract
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].
| Original language | English |
|---|---|
| Pages (from-to) | 453-459 |
| Number of pages | 7 |
| Journal | Discrete Mathematics |
| Volume | 313 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jan 1 2013 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
Cite this
Independent arborescences in directed graphs. / Frank, András; Fujishige, Satoru; Kamiyama, Naoyuki; Katoh, Naoki.
In: Discrete Mathematics, Vol. 313, No. 4, 01.01.2013, p. 453-459.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Independent arborescences in directed graphs
AU - Frank, András
AU - Fujishige, Satoru
AU - Kamiyama, Naoyuki
AU - Katoh, Naoki
PY - 2013/1/1
Y1 - 2013/1/1
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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UR - http://www.scopus.com/inward/citedby.url?scp=84870696714&partnerID=8YFLogxK
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 -