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Combinatorial Optimization pp 271–289Cite as

b-Matchings and T-Joins

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Part of the book series: Algorithms and Combinatorics 21 ((AC,volume 21))

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References

General Literature

  • Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., and Schrijver, A. [1998]: Combinatorial Optimization. Wiley, New York 1998, Sections 5.4 and 5.5

    MATH  Google Scholar 

  • Frank, A. [1996]: A survey on T-joins, T-cuts, and conservative weightings. In: Combinatorics, Paul Erdős is Eighty; Volume 2 (D. Miklós, V.T. Sós, T. Szőnyi, eds.), Bolyai Society, Budapest 1996, pp. 213–252

    Google Scholar 

  • Gerards, A.M.H. [1995]: Matching. In: Handbooks in Operations Research and Management Science; Volume 7: Network Models (M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser, eds.), Elsevier, Amsterdam 1995, pp. 135–224

    Google Scholar 

  • Lovász, L., and Plummer, M.D. [1986]: Matching Theory. Akadémiai Kiadó, Budapest 1986, and North-Holland, Amsterdam 1986

    MATH  Google Scholar 

  • Schrijver, A. [1983]: Min-max results in combinatorial optimization; Section 6. In: Mathematical Programming; The State of the Art-Bonn 1982 (A. Bachem, M. Grötschel, B. Korte, eds.), Springer, Berlin 1983, pp. 439–500

    Google Scholar 

  • Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin 2003, Chapters 29-33

    MATH  Google Scholar 

Cited References

  • Anstee, R.P. [1987]: A polynomial algorithm for b-matchings: an alternative approach. Information Processing Letters 24 (1987), 153–157

    Article  MathSciNet  MATH  Google Scholar 

  • Caprara, A., and Fischetti, M. [1996]: 0, 1/2-Chvátal-Gomory cuts. Mathematical Programming 74 (1996), 221–235

    Article  MathSciNet  Google Scholar 

  • Edmonds, J. [1965]: Maximum matching and a polyhedron with (0,1) vertices. Journal of Research of the National Bureau of Standards B 69 (1965), 125–130

    MathSciNet  MATH  Google Scholar 

  • Edmonds, J., and Johnson, E.L. [1970]: Matching: A well-solved class of integer linear programs. In: Combinatorial Structures and Their Applications; Proceedings of the Calgary International Conference on Combinatorial Structures and Their Applications 1969 (R. Guy, H. Hanani, N. Sauer, J. Schonheim, eds.), Gordon and Breach, New York 1970, pp. 69–87

    Google Scholar 

  • Edmonds, J., and Johnson, E.L. [1973]: Matching, Euler tours and the Chinese postman problem. Mathematical Programming 5 (1973), 88–124

    Article  MathSciNet  MATH  Google Scholar 

  • Guan, M. [1962]: Graphic programming using odd and even points. Chinese Mathematics 1 (1962), 273–277

    Google Scholar 

  • Hadlock, F. [1975]: Finding a maximum cut of a planar graph in polynomial time. SIAM Journal on Computing 4 (1975), 221–225

    Article  MathSciNet  MATH  Google Scholar 

  • Letchford, A.N., Reinelt, G., and Theis, D.O. [2004]: A faster exact separation algorithm for blossom inequalities. Proceedings of the 10th Conference on Integer Programming and Combinatorial Optimization; LNCS 3064 (D. Bienstock, G. Nemhauser, eds.), Springer, Berlin 2004, pp. 196–205

    Google Scholar 

  • Marsh, A.B. [1979]: Matching algorithms. Ph.D. thesis, Johns Hopkins University, Baltimore 1979

    Google Scholar 

  • Padberg, M.W., and Rao, M.R. [1982]: Odd minimum cut-sets and b-matchings. Mathematics of Operations Research 7 (1982), 67–80

    Article  MathSciNet  MATH  Google Scholar 

  • Pulleyblank, W.R. [1973]: Faces of matching polyhedra. Ph.D. thesis, University of Waterloo, 1973

    Google Scholar 

  • Pulleyblank, W.R. [1980]: Dual integrality in b-matching problems. Mathematical Programming Study 12 (1980), 176–196

    MathSciNet  MATH  Google Scholar 

  • Rizzi, R. [2002]: Minimum T-cuts and optimal T-pairings. Discrete Mathematics 257 (2002), 177–181

    Article  MathSciNet  MATH  Google Scholar 

  • Sebő, A. [1987]: A quick proof of Seymour’s theorem on T-joins. Discrete Mathematics 64 (1987), 101–103

    MathSciNet  Google Scholar 

  • Seymour, P.D. [1981]: On odd cuts and multicommodity flows. Proceedings of the London Mathematical Society (3) 42 (1981), 178–192

    MathSciNet  MATH  Google Scholar 

  • Tutte, W.T. [1952]: The factors of graphs. Canadian Journal of Mathematics 4 (1952), 314–328

    MathSciNet  MATH  Google Scholar 

  • Tutte, W.T. [1954]: A short proof of the factor theorem for finite graphs. Canadian Journal of Mathematics 6 (1954), 347–352

    MathSciNet  MATH  Google Scholar 

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(2006). b-Matchings and T-Joins. In: Combinatorial Optimization. Algorithms and Combinatorics 21, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29297-7_12

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