On intersecting hypergraphs
نویسندگان
چکیده
منابع مشابه
On 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 ...
متن کاملOn Randomly Generated Intersecting Hypergraphs
An intersecting hypergraph is one in which each pair of edges has a nonempty intersection. Here, we consider r-uniform hypergraphs which are those for which all edges contain r vertices. ∗Supported in part by NSF grant DMS-0100400. †Supported in part by NSF grant CCR-9818411. ‡Supported in part by NSF VIGRE grant DMS-9819950. §Research was partially supported by OTKA Grants T 030059, T 029074, ...
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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...
متن کاملOn Randomly Generated Non-Trivially Intersecting Hypergraphs
We propose two procedures to choose members of ([n] r ) sequentially at random to form a non-trivially intersecting hypergraph. In both cases we show what is the limiting probability that if r = cnn 1/3 with cn → c, then the process results in a Hilton-Milner-type hypergraph.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00136-2