A Theorem on Flows in Networks

  • David Gale
Part of the Modern Birkhäuser Classics book series (MBC)


The theorem to be proved in this note is a generalization of a well-known combinatorial theorem of P. Hall, [4].


Aggregate Demand Nonnegative Real Number Rand Corporation Capacity Function Dual Sequence 


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  1. 1.
    G. B. Dantzig and D. R. Fulkerson, On the ma.x-flow min-cut theorem of networks,Ann. of Math. Study No. 38, Contributions to linear inequalities and related topics,edited by H. W. Kuhn and A. W. Tucker, 215-221.Google Scholar
  2. 2.
    L. R. Ford, Jr., and D. R. Fulkerson, Maximal flow through a network,Canad. J. Math. 8 (1956), 399-404.MATHMathSciNetGoogle Scholar
  3. 3.
    L. R. Ford, Jr., and D. R. Fulkerson, A simple algorithm for finding maximal network flows aud an application to the Hitchcock problem,Canad. J. Math. 9 (1957), 210-218.MATHGoogle Scholar
  4. 4.
    P. Hall. On Representatives of Subsets,J. London Math. Soc, 10 (1935), 26-30.MATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • David Gale
    • 1
  1. 1.The Rand Corporation and Brown UniversityUSA

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