Independent arborescences in directed graphs

András Frank, Satoru Fujishige, Naoyuki Kamiyama, Naoki Katoh

研究成果: ジャーナルへの寄稿学術誌査読

抄録

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].

本文言語英語
ページ(範囲)453-459
ページ数7
ジャーナルDiscrete Mathematics
313
4
DOI
出版ステータス出版済み - 2013

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • 離散数学と組合せ数学

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