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Characterizing matchings as the intersection of matroids

Author

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  • Sándor P. Fekete
  • Robert T. Firla
  • Bianca Spille

Abstract

This paper deals with the problem of representing the matching independence system in a graph as the intersection of finitely many matroids. After characterizing the graphs for which the matching independence system is the intersection of two matroids, we study the function μ(G), which is the minimum number of matroids that need to be intersected in order to obtain the set of matchings on a graph G, and examine the maximal value, μ(n), for graphs with n vertices. We describe an integer programming formulation for deciding whether μ(G)≤k. Using combinatorial arguments, we prove that μ(n)∈Ω(log logn). On the other hand, we establish that μ(n)∈O(logn/ log logn). Finally, we prove that μ(n)=4 for n=5,…,12, and sketch a proof of μ(n)=5 for n=13,14,15. Copyright Springer-Verlag 2003

Suggested Citation

  • Sándor P. Fekete & Robert T. Firla & Bianca Spille, 2003. "Characterizing matchings as the intersection of matroids," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 319-329, November.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:2:p:319-329
    DOI: 10.1007/s001860300301
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    Cited by:

    1. D. Magos & I. Mourtos & L. Pitsoulis, 2009. "Persistency and matroid intersection," Computational Management Science, Springer, vol. 6(4), pages 435-445, October.

    More about this item

    Keywords

    matching; matroid intersection; 05B35; 05C70; 90C27;
    All these keywords.

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