منابع مشابه
Chain Intersecting Families
Let F be a family of subsets of an n-element set. F is called (p,q)-chain intersecting if it does not contain chains A1 ( A2 ( · · · ( Ap and B1 ( B2 ( · · · ( Bq with Ap∩Bq = ∅. The maximum size of these families is determined in this paper. Similarly to the p = q = 1 special case (intersecting families) this depends on the notion of r-complementing-chain-pair-free families, where r = p + q − ...
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We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families F of k-element subsets of [n] := {1, . . . , n}, such that every element of [n] lies in the same (or approximately the same) number of members of F . In particular, we show that we can guarantee |F| = o( ( n−1 k−1 ) ) if and only if k = o(n).
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Let G be a graph on vertex set [n], and for X [n] let N(X) be the union of X and it's neighborhood in G. A family of sets F 2 is G-intersecting if N(X) \ Y 6= ; for all X;Y 2 F . In this paper we study the cardinality and structure of the largest k-uniform G-intersecting families on a xed graph G.
متن کاملMultiply-intersecting families
Intersection problems occupy an important place in the theory of finite sets. One of the central notions is that of a r-wise r-intersecting family, that is, a collection holds for all choices of 1 < il < < i, < m. What is the maximal size m = m(n, r, t) of a r-wise t-intersecting family? Taking all subsets containing a fixed t-element set shows that m(n, r, 1) > 2 "-' holds for all n 3 f 2 0. O...
متن کاملEnumeration of intersecting families
For a natural number m, let m =11,2, . . ., m} . An intersecting family on m is a set A of sets such that U A g m and any two members of A have non-empty intersection . We let J_ be the set of all maximal intersecting families on m . We are concerned with estimating JJ . J . In Section 2 we obtain a lower bound by elementary counting methods . In Section 3 we obtain an upper bound using a resul...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00439-9