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, log in via an institution to check access.
Similar content being viewed by others
References
A.Björner and L.Lovász,Pseudomodular Lattices and Continuous Matroids, 1986.
A. Dress andL. Lovász, On some Combinatorial Properties of Algebraic Matroids.Combinatorica,7 (1987), 39–48.
A. W.Ingleton and R. A.Main, Non-algebraic Matroids exist.Bull. London Math. Soc.,7 (75) 144–146.
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.
Author information
Authors and Affiliations
Additional information
Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02124676