Uniform Intersecting Families with Covering Number Restrictions
نویسندگان
چکیده
It is known that any k-uniform family with covering number t has at most k t t-covers. In this paper, we give better upper bounds for the number of t-covers in k-uniform intersecting families with covering number t.
منابع مشابه
Covers in Uniform Intersecting Families and a Counterexample to a Conjecture of Lovász
We discuss the maximum size of uniform intersecting families with covering number at least . Among others, we construct a large k-uniform intersecting family with covering number k, which provides a counterexample to a conjecture of Lov asz. The construction for odd k can be visualized on an annulus, while for even k on a Mobius band.
متن کاملCovers in 5-uniform intersecting families with covering number three
Let k be an integer. It is known that the maximum number of threecovers of a k-uniform intersecting family with covering number three is k − 3k + 6k − 4 for k = 3, 4 or k ≥ 9. In this paper, we prove that the same holds for k = 5, and show that a 5-uniform intersecting family with covering number three which has 76 three-covers is uniquely determined.
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 کاملIntersecting Families — Uniform versus Weighted
What is the maximal size of k-uniform r-wise t-intersecting families? We show that this problem is essentially equivalent to determine the maximal weight of non-uniform r-wise t-intersecting families. Some EKR type examples and their applications are included.
متن کاملIsomorphism Classes of Maximal Intersecting Uniform Families Are Few
Denote by f(k,m) the number of isomorphism classes of maximal intersecting k-uniform families of subsets of [m]. In this note we prove the existence of a constant f(k) such that f(k,m) ≤ f(k) for all values of m.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 7 شماره
صفحات -
تاریخ انتشار 1998