Erdos-Ko-Rado for three sets
نویسنده
چکیده
Fix integers k ≥ 3 and n ≥ 3k/2. Let F be a family of k-sets of an n-element set so that whenever A,B, C ∈ F satisfy |A ∪ B ∪ C| ≤ 2k, we have A ∩ B ∩ C 6= ∅. We prove that |F| ≤ (n−1 k−1 ) with equality only when ⋂ F∈F F 6= ∅. This settles a conjecture of Frankl and Füredi [2], who proved the result for n ≥ k + 3k.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 113 شماره
صفحات -
تاریخ انتشار 2006