Regularity Conditions and Intersecting Hypergraphs
نویسندگان
چکیده
منابع مشابه
Hypergraphs, Quasi-randomness, and Conditions for Regularity
Haviland and Thomason and Chung and Graham were the first to investigate systematically some properties of quasi-random hypergraphs. In particular, in a series of articles, Chung and Graham considered several quite disparate properties of random-like hypergraphs of density 1/2 and proved that they are in fact equivalent. The central concept in their work turned out to be the so called deviation...
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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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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...
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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 ...
متن کاملCross-intersecting pairs of hypergraphs
Two hypergraphs H1, H2 are called cross-intersecting if e1 ∩ e2 ̸= ∅ for every pair of edges e1 ∈ H1, e2 ∈ H2. Each of the hypergraphs is then said to block the other. Given integers n, r,m we determine the maximal size of a sub-hypergraph of [n]r (meaning that it is r-partite, with all sides of size n) for which there exists a blocking sub-hypergraph of [n]r of size m. The answer involves a sel...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1981
ISSN: 0002-9939
DOI: 10.2307/2043332