Most Probably Intersecting Hypergraphs
نویسندگان
چکیده
منابع مشابه
Most Probably Intersecting Hypergraphs
The celebrated Erdős-Ko-Rado theorem shows that for n > 2k the largest intersecting k-uniform set family on [n] has size ( n−1 k−1 ) . It is natural to ask how far from intersecting larger set families must be. Katona, Katona and Katona introduced the notion of most probably intersecting families, which maximise the probability of random subfamilies being intersecting. We consider the most prob...
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Let F be a family of an n-element set. It is called intersecting if every pair of its members have a non-disjoint intersection. It is wellknown that an intersecting family satisfies the inequality |F| ≤ 2n−1. Suppose that |F| = 2n−1+i. Choose the members of F independently with probability p (delete them with probability 1−p). The new family is intersecting with a certain probability. We try to...
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A family A of sets is said to be intersecting if A ∩ B 6= ∅ for all A, B ∈ A. It is a well-known and simple fact that an intersecting family of subsets of [n] = {1, 2, . . . , n} can contain at most 2n−1 sets. Katona, Katona and Katona ask the following question. Suppose instead A ⊂ P[n] satisfies |A| = 2n−1 + i for some fixed i > 0. Create a new family Ap by choosing each member of A independe...
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A hypergraph is 2-intersecting if any two edges intersect in at least two vertices. Blais, Weinstein and Yoshida asked (as a first step to a more general problem) whether every 2-intersecting hypergraph has a vertex coloring with a constant number of colors so that each hyperedge has at least min{|e|, 3} colors. We show that there is such a coloring with at most 5 colors (which is best possible...
متن کاملOn intersecting hypergraphs
We investigate the following question: “Given an intersecting multi-hypergraph on n points, what fraction of edges must be covered by any of the best 2 points?” (Here “best” means that together they cover the most.) We call this M2(n). This is a special case of a question asked by Erdős and Gyárfás [1] (they considered r–wise intersecting and the best t points), and is a generalization of work ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4784