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Some combinatorial applications of the new linear programming algorithm

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Combinatorics and Graph Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 885))

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References

  1. J. Edmonds, Maximum matching and a polyhedron with 0,1-vertices, J. Res. Nat. Bur. Stan. B 69(1965), 125–130.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Edmonds, Optimum branchings, J. Res. Nat. Bur. Stan. B 71(1967), 233–240.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Edmonds, Submodular functions, matroids, and certain polyhedra, in: Combinatorial Structures and their Appl. (Proc. Intern. Conf. Calgary, 1969 R. Guy, H. Hanani, N. Sauer, J. Schönheim, eds.), Gordon and Breach, N.Y. 1970, 69–87.

    Google Scholar 

  4. J. Edmonds, Edge-disjoint branchings, in: Combinatorial Algorithms (Courant Comp. Sci. Symp. Monterey, 1972; R. Rustin, ed.) Academic Press, N.Y. 1973, 91–96.

    Google Scholar 

  5. J. Edmonds, Matroid intersection, Annals of Disctrete Math., 4 (1979), 39–49.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Edmonds and R. Giles, A min-max relation for submodular functions on graphs, Annals of Discrete Math., 1 (1977), 185–204.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Edmonds and E.L. Johnson, Matching, Euler tours, and the Chinese postman, Math. Prog., 5 (1973), 88–124.

    Article  MathSciNet  MATH  Google Scholar 

  8. L.R. Ford and D.R. Fulkerson, Flows in Networks, Princeton Univ. Press, Princeton, N.J. 1962.

    MATH  Google Scholar 

  9. A. Frank, Kernel systems of directed graphs, Acta Sci. Math. Szeged 41 (1979), 63–76.

    MathSciNet  MATH  Google Scholar 

  10. A. Frank, How to make a digraph strongly connected? Combinatorica (submitted).

    Google Scholar 

  11. D.R. Fulkerson, Packing rooted directed cuts in weighted directed graphs, Math. Prog., 6 (1974), 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  12. D.R. Fulkerson, Anti-blocking polyhedra, J. Combinatorial Theory, B 12 (1972), 50–71.

    Article  MathSciNet  MATH  Google Scholar 

  13. P. Gács and L. Lovász, Khachiyan’s algorithm for linear programming, Math. Prog. Studies (submitted).

    Google Scholar 

  14. M. Grötschel, L. Lovász and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica (submitted).

    Google Scholar 

  15. A.V. Karzanov, On the minimal number of arcs of a digraph meeting all its directed cut sets. (To appear).

    Google Scholar 

  16. L.G. Khachiyan, A polynomial algorithm in linear programming, Dokl. Akad. Nauk SSSR 244 (1979), 1093–1096.

    MathSciNet  MATH  Google Scholar 

  17. E.L. Lawler, Optimal matroid intersections, in: Combinatorial Structures and their Applications (Proc. Intern. Conf. Calgary, 1969; R. Guy, H. Hanani, N. Sauer, J. Schönheim, eds.), Gordon and Breach, N.Y. 1970, 233–235.

    Google Scholar 

  18. L. Lovász, On the Shannon capacity of a graph, IEEE Trans. on Inf. Theory, 25 (1979), 1–7.

    Article  MathSciNet  MATH  Google Scholar 

  19. C.L. Lucchesi, A minimax equality for directed graphs, Thesis, University of Waterloo, 1976.

    Google Scholar 

  20. C.L. Lucchesi and D.H. Younger, A minimax relation for directed graphs, J. London Math. Soc., 17 (1978), 369–374.

    Article  MathSciNet  MATH  Google Scholar 

  21. M.W. Padberg and M.R. Rao, Minimum cut-sets and b-matchings, (to appear).

    Google Scholar 

  22. N.Z. Shor, Convergence rate of the gradient desent method with dilatation of the space, Kibernetika 2 (1970), 80–85.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematical Institute, A. Jozsef University, Szeged

    L. Lovasz

  2. Amsterdam

    A. Schriver

Authors
  1. L. Lovasz
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  2. A. Schriver
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Editor information

Siddani Bhaskara Rao

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© 1981 Springer-Verlag

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Lovasz, L., Schriver, A. (1981). Some combinatorial applications of the new linear programming algorithm. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092253

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  • DOI: https://doi.org/10.1007/BFb0092253

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11151-1

  • Online ISBN: 978-3-540-47037-3

  • eBook Packages: Springer Book Archive

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