The Maximum Size of 3-Wise Intersecting and 3-Wise Union Families
نویسندگان
چکیده
منابع مشابه
The Maximum Size of 3-Wise Intersecting and 3-Wise Union Families
Let F be an n-uniform hypergraph on 2n vertices. Suppose that |F1 ∩ F2 ∩ F3| ≥ 1 and |F1 ∪ F2 ∪ F3| ≤ 2n− 1 holds for all F1, F2, F3 ∈ F . We prove that the size of F is at most ( 2n−2 n−1 ) .
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A family of sets is said to be symmetric if its automorphism group is transitive, and 3-wise intersecting if any three sets in the family have nonempty intersection. Frankl conjectured in 1981 that if A is a symmetric 3-wise intersecting family of subsets of {1, 2, . . . , n}, then |A| = o(2). Here, we give a short proof of Frankl’s conjecture using a sharp threshold result of Friedgut and Kalai.
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2006
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-006-0655-2