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- 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.
- Bondy, Adrian; Murty, U.S.R. (2008), Graph Theory, Graduate Texts in Mathematics 244, Springer, p. 195, ISBN 9781846289699.
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