Independence system
In combinatorial mathematics, an independence system S is a pair (E, I), where E is a finite set and I is a collection of subsets of E (called the independent sets) with the following properties:
The empty set is independent, i.e., ∅ ∈ I. (Alternatively, at least one subset of E is independent, i.e., I ≠ ∅.)
Every subset of an independent set is independent, i.e., for each E' ⊆ E, E ∈ I → E' ∈ I. This is sometimes called the hereditary property.
Adding the augmentation property or the independent set exchange property yields a matroid.
For a more general description, see abstract simplicial complex.
References
Bondy, Adrian; Murty, U.S.R. (2008), Graph Theory, Graduate Texts in Mathematics 244, Springer, p. 195, ISBN 9781846289699 .