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This problem is NP-complete, a nice reference is this answer here by András Salamon: https://cstheory.stackexchange.com/a/356/419
If you are interested in results about the complete family, see [Baranyai's theorem].1Baranyai's theorem.
If you are interested in results about the complete family, see [Baranyai's theorem].1
If you are interested in results about the complete family, see Baranyai's theorem.
