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Perfect Matching and Polymatroids

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Cybernetics and Systems Analysis Aims and scope

Abstract

It is shown that any graph has a perfect matching if and only if a specially defined vector is the base of extended polymatroid associated with submodular function defined on subsets of vertex set. Based on this fact, different algorithms for testing flow feasibility can be used to find some perfect matching in a given graph.

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References

  1. L. Lóvasz and M. D. Plummer, Matching Theory, AMS Chelsea Publ., Providence (2009).

    MATH  Google Scholar 

  2. M. Grotschel, L. Lovasz, and A. Schrijer, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, Berlin (1988).

    Book  Google Scholar 

  3. F. A. Sharifov, “Perfect matchings and extended polymatroid,” Cybern. Syst. Analysis, Vol. 44, No. 3, 452–456 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Sharifov, “Perfectly matchable subgraph problem on a bipartite graph,” RAIRO, Operation Research, Vol. 44, No. 1, 27–42 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  5. R. B. Handfield and E. L. Nichols, Jr., Reorganization of Supply Chains. Development of Integrated Systems of Value Creation [in Russian], Izd. Dom Vilyams, Moscow (2003).

  6. X. Brusset, “Estimating the supply chain efficiency loss when the seller has to estimate the buyer’s willingness to pay,” RAIRO, Operation Research, Vol. 48, No. 4, 477–496 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  7. F. A. Sharifov and N. J. Krivitska, “Economic–mathematic problems in planning supply chain,” Ekonomika, Menedzhment, Biznes, No. 1 (19), 61–69 (2014).

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    F. A. Sharifov

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  1. F. A. Sharifov
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Correspondence to F. A. Sharifov.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2017, pp. 113–119.

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Sharifov, F.A. Perfect Matching and Polymatroids. Cybern Syst Anal 53, 753–758 (2017). https://doi.org/10.1007/s10559-017-9977-8

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  • DOI: https://doi.org/10.1007/s10559-017-9977-8

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