by Firla, Robert T., Spille, Bianca.

**Series:** 2000-17, Preprints

- MSC:
- 90C10 Integer programming
- 90C27 Combinatorial optimization
- 05B35 Matroids, geometric lattices
- 05C70 Factorization, matching, partitioning, covering and packing

**Abstract:**

The set of matchings in a graph is an independence system

and, hence, the intersection of finitely many matroids.

We are interested in lower and upper bounds on the number

of matroids needed to represent it.

We characterize the graphs for which the set of matchings

is the intersection of two matroids and show that

the set of matchings on $K_5$ is not the intersection

of at most three matroids.

Furthermore, we prove upper bounds on the number of

matroids.

**Keywords:**

matching, matroid intersection, circuit-graph