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Matroid: a matroid M on a ground set E is a pair (S, l), where l is a collection of subsets of S (called the independent sets) with the following properties:

1. The empty set is independent.

2. Every subset of an independent set is independent; this is sometimes called the hereditary property.

3. If A and B are two independent sets and A has more elements than B, then there exists an element in A which is not in B and when added to B still gives an independent set; this property is called the exchange property.

1. Let G=(V,E) be an undirected graph. Let the set S=E and the independent sets corresponding to acyclic subgraphs with at most two edges is a subset.