Some Aspects of Duality in Combinatorial Optimization

  • E. L. Lawler
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 175)


The literature of combinatorial optimization, and of related fields such as graph theory. is replete with numerous examples of duality theorems and their applications: the Max-Flow Min-Cut Theorem, König-Egervary Theorem, Edmond’s Odd Set Covering Theorem, Hoffman’s Circulation Theorem, Minty’s Painting Theorem, Menger’s Theorem, Dilworth’s Theorem, etc. Our objective in this Chapter is to review a few of these duality results and to give some examples which may be convincing of the usefulness of duality concepts in problem formulation and solution.


Feasible Solution Acyclic Directed Graph Duality Theorem Minimal Solution Graphic Duality 
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  1. [1]
    M.L. Balinski, short note, Mgt. Sci. (1971).Google Scholar
  2. [2]
    R.P. Dilworth, “A Decomposition Theorem for Partially Ordered Sets”, Ann. of Math., 51 (1950), 161–166.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    J.D. Muchland, unpublished memorandum (1968).Google Scholar

Copyright information

© CISM, Udine 1975

Authors and Affiliations

  • E. L. Lawler
    • 1
  1. 1.Dept. of Electrical Engineering and Computer ScienceUniversity of California at BerkeleyUSA

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