The maximum size of 4-wise 2-intersecting and 4-wise 2-union families
نویسندگان
چکیده
منابع مشابه
The maximum size of 4-wise 2-intersecting and 4-wise 2-union families
Let F be an n-uniform hypergraph on 2n vertices. Suppose that |F1∩F2∩F3∩F4| ≥ 2 and |F1∪F2∪F3∪ F4| ≤ n−2 holds for all F1,F2,F3,F4 ∈F . We prove that the size of F is at most (2n−4 n−2 ) for n sufficiently large.
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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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متن کاملEKR type inequalities for 4-wise intersecting families
Let 1 ≤ t ≤ 7 be an integer and let F be a k-uniform hypergraph on n vertices. Suppose that |A∩B∩C∩D| ≥ t holds for all A,B,C,D ∈ F . Then we have |F | ≤ (n−t k−t ) if | k n − 2 |< ε holds for some ε > 0 and all n > n0(ε). We apply this result to get EKR type inequalities for “intersecting and union families” and “intersecting Sperner families.”
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2006
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2005.05.005