Matroid matching in pseudomodular lattices

Abstract

The matroid matching problem (also known as matroid parity problem) has been intensively studied by several authors. Starting from very special problems, in particular the matching problem and the matroid intersection problem, good characterizations have been obtained for more and more general classes of matroids. The two most recent ones are the class of representable matroids and, later on, the class of algebraic matroids (cf. [4] and [2]). We present a further step of generalization, showing that a good characterization can also be obtained for the class of socalled pseudomodular matroids, introduced by Björner and Lovász (cf. [1]). A small counterexample is included to show that pseudomodularity still does not cover all matroids that behave well with respect to matroid matching.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    A.Björner and L.Lovász,Pseudomodular Lattices and Continuous Matroids, 1986.

  2. [2]

    A. Dress andL. Lovász, On some Combinatorial Properties of Algebraic Matroids.Combinatorica,7 (1987), 39–48.

    Google Scholar 

  3. [3]

    A. W.Ingleton and R. A.Main, Non-algebraic Matroids exist.Bull. London Math. Soc.,7 (75) 144–146.

  4. [4]

    L.Lovász, Selecting Independent Lines from a Family of Lines in Projective Space.Acta Sci. Math. 42 (80) 121–131. See [2] for further references.

Download references

Author information

Affiliations

Authors

Additional information

Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hochstättler, W., Kern, W. Matroid matching in pseudomodular lattices. Combinatorica 9, 145–152 (1989). https://doi.org/10.1007/BF02124676

Download citation

AMS subject classification (1980)

  • 05 B 35