Critical hypergraphs and intersecting set-pair systems
نویسندگان
چکیده
منابع مشابه
Union-Intersecting Set Systems
Three intersection theorems are proved. First, we determine the size of the largest set system, where the system of the pairwise unions is l-intersecting. Then we investigate set systems where the union of any s sets intersect the union of any t sets. The maximal size of such a set system is determined exactly if s + t ≤ 4, and asymptotically if s + t ≥ 5. Finally, we exactly determine the maxi...
متن کاملMost 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...
متن کاملColoring 2-Intersecting Hypergraphs
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 ...
متن کاملIntersecting set systems and graphic matroids,
Two simple proofs are given to an earlier partial result about an extremal set theoretic conjecture of Chung, Frank!, Graham, Shearer and Faudree, Schelp, S6s, respectively. The statement is slightly strengthened within a matroid theoretic framework. The first proof re lies on results from matroid theory, while the second is based on an explicit constJuction providing an elementary proof. @ 199...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1985
ISSN: 0095-8956
DOI: 10.1016/0095-8956(85)90043-7