Advertisement

Classical Work: Edge-Disjoint Branchings, Min-Max Theorems, and Shortest Connection Networks

  • Rudolf AhlswedeEmail author
Chapter
Part of the Foundations in Signal Processing, Communications and Networking book series (SIGNAL, volume 15)

Abstract

Let \(\mathcal {G}\) be a directed graph, and let r be a specified node in \(\mathcal {G}\). A branching B in \(\mathcal {G}\) rooted at r is a spanning tree of \(\mathcal {G}\) such that, for every node v, \(v\ne r\), there is exactly one edge of B which is directed towards v.

References

  1. 1.
    L. Lovász, On two minimax theorems in graph. J. Combin. Theory (B) 21, 96–103 (1976)MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Edmonds, Edge-disjoint branchings, Combinatorial Algorithms (Courant Comput. Sci. Sympos., Vol. 9, New York Univ., New York, 1972), pp. 91–96 (Algorithmics, New York, 1973)Google Scholar
  3. 3.
    C. Lucchesi and D.H. Younger, A minimax theorem for directed graphs, to appearGoogle Scholar
  4. 4.
    I.P. McWhirter, D.H. Younger, Strong covering of a bipartite graph. J. Lond. Math. Soc. 2, 86–90 (1971)MathSciNetCrossRefGoogle Scholar
  5. 5.
    L. Lovász, Minimax theorems for hypergraphs. in Hypergraph Seminar (Lecture Notes in Math, 411) (Springer, New York, 1974), pp. 111–126CrossRefGoogle Scholar
  6. 6.
    C. Berge, Graphs and Hypergraphs (American- Elsevier, New York, 1973)Google Scholar
  7. 7.
    D.R. Fulkerson, Packing rooted directed cuts in a weighted directed graph, Technical report No. 157, Dept. of Operations Research, Cornell UniversityGoogle Scholar
  8. 8.
    O. Boruvka, On a minimal problem, vol. 3. Práce Moravské Pridovedecké Spolecnosti (1926)Google Scholar
  9. 9.
    J.B. Kruskal, On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7, 48–50 (1956)MathSciNetCrossRefGoogle Scholar
  10. 10.
    R. Courant, H. Robbins, What is Mathematics, 4th edn. (Oxford University, N.Y., 374 et seq., 1941)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.BielefeldGermany

Personalised recommendations