Mathematical Methods of Operations Research

, Volume 58, Issue 2, pp 319–329

Characterizing matchings as the intersection of matroids

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

DOI: 10.1007/s001860300301

Cite this article as:
Fekete, S., Firla, R. & Spille, B. Math Meth Oper Res (2003) 58: 319. doi:10.1007/s001860300301


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.


matchingmatroid intersection

AMS Subject Classification


Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  • Sándor P. Fekete
    • 1
  • Robert T. Firla
    • 2
  • Bianca Spille
    • 1
  1. 1.Abteilung für Mathematische OptimierungTU BraunschweigBraunschweigGermany
  2. 2.Institut für Mathematische OptimierungOtto-von-Guericke-Universität MagdeburgMagdeburgGermany