Two Results on Union-Closed Families
نویسنده
چکیده
We show that there is some absolute constant c > 0, such that for any union-closed family F ⊆ 2, if |F| ≥ ( 1 2 − c)2n, then there is some element i ∈ [n] that appears in at least half of the sets of F . We also show that for any union-closed family F ⊆ 2, the number of sets which are not in F that cover a set in F is at most 2, and provide examples where the inequality is tight.
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تاریخ انتشار 2017