منابع مشابه
On cross-intersecting families
Frankl, P., On cross-intersecting families, Discrete Mathematics 108 (1992) 291-295. Let n 3 t z 1 be integers. Let 9, YI be families of subsets of the n-element set X. They are called cross t-intersecting if IF n GI 2 t holds for all F E 9 and G E 3. If 9 = CfI then 9 is called t-intersecting. Let m(n, t) denote the maximum possible cardinality of a r-intersecting family. Our main result says ...
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Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be `-cross-intersecting iff |A∩B| = ` for all A ∈ A and B ∈ B. Denote by P`(n) the maximum value of |A||B| over all such pairs. The best known upper bound on P`(n) is Θ(2), by Frankl and Rödl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2`, a simple construction of an `-cross-intersectin...
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For all p, t with 0 < p < 0.11 and 1≤ t ≤ 1/(2p), there exists n0 such that for all n,k with n > n0 and k/n = p the following holds: if A and B are k-uniform families on n vertices, and |A∩B| ≥ t holds for all A ∈A and B ∈B, then |A ||B| ≤ (n−t k−t )2 .
متن کاملOn Cross-intersecting Families of Sets
A family A of ‘-element subsets and a family B of k-element subsets of an n-element set are cross-intersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product jAjjBj, and give a new and short proof for one of them. We also determine the maximum of jAjx‘ þ jBjxk for arbitrary...
متن کاملOn Cross-Intersecting Families of Set Partitions
Let B(n) denote the collection of all set partitions of [n]. Suppose A1,A2 ⊆ B(n) are cross-intersecting i.e. for all A1 ∈ A1 and A2 ∈ A2, we have A1 ∩A2 6= ∅. It is proved that for sufficiently large n,
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90682-6