Intersection (Matroid)

discrete-mathematics combinatorics

Definition

Intersection (Matroid)

Let ${\mathcal{M}}_1=(E,{\mathcal{I}}_1)$ and ${\mathcal{M}}_2=(E,{\mathcal{I}}_2)$ be two matroids over the same ground set $E$. The intersection of these two matroids is

$${\mathcal{M}}_1\cap {\mathcal{M}}_2=(E,{\mathcal{I}}_1\cap {\mathcal{I}}_2).$$

The intersection of two matroids is in general not a matroid.