Matroids

An independence system $(E,\mathcal{I})$ is called a matroid if:

1. $\varnothing \in \mathcal{I}$
2. for all $A\in \mathcal{L}$ and $B\subseteq A$, we have $B\in \mathcal{I}$
3. for all $A,B\in \mathcal{L}$ with $|A|<|B|$, there exists an element $b\in B\backslash A$ such that $A\cup \{b\}\in \mathcal{I}$

summe der teilmenge

Bases of a Matroid
Uniform Matroids
Partition Matroids
Linear Matroids
Graphic Matroids
Matching Matroids

The Rank of a Matroid
Characterizations of Matroids

Matroid optimization