A note on disjoint arborescences


Recently Kamiyama, Katoh, and Takizawa have shown a theorem on packing arc-disjoint arborescences that is a proper extension of Edmonds’ theorem on disjoint spanning branchings. We show a further extension of their theorem, which makes clear an essential rôle of a reachability condition played in the theorem. The right concept required for the further extension is “convexity” instead of “reachability”.

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  1. [1]

    K. Bérczi and A. Frank: Variations for Lovász’ submodular ideas, Technical Report TR-2008-7, The Egerváry Research Group on Combinatorial Optimization (June 2008).

  2. [2]

    J. Edmonds: Edge-disjoint branchings, in: Combinatorial Algorithms (B. Rustin, ed.), Academic Press, 1973, pp. 91–96.

  3. [3]

    N. Kamiyama, N. Katoh and A. Takizawa: Arc-disjoint in-trees in directed graphs, Combinatorica29(2) (2009), 197–214.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    A. Schrijver: Combinatorial Optimization — Polyhedra and Efficiency, Springer, 2003.

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Correspondence to Satoru Fujishige.

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Fujishige, S. A note on disjoint arborescences. Combinatorica 30, 247–252 (2010). https://doi.org/10.1007/s00493-010-2518-y

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Mathematics Subject Classification (2000)

  • 05C70
  • 05C20
  • 05C40
  • 90C27