An Erdős-Ko-Rado Theorem for Multisets
نویسندگان
چکیده
منابع مشابه
An Erdös-Ko-Rado theorem for multisets
Let k and m be positive integers. A collection of k-multisets from {1, . . . ,m} is intersecting if every pair of multisets from the collection is intersecting. We prove that for m ≥ k +1, the size of the largest such collection is ( m+k−2 k−1 ) and that when m > k + 1, only a collection of all the k-multisets containing a fixed element will attain this bound. The size and structure of the larg...
متن کاملAn Erdős-Ko-Rado theorem for cross t-intersecting families
Article history: Received 28 January 2013 Available online 27 September 2014
متن کاملA product version of the Erdős-Ko-Rado theorem
Let F1, . . . ,Fr ⊂ ([n] k ) be r-cross t-intersecting, that is, |F1 ∩ ·· · ∩Fr| ≥ t holds for all F1 ∈ F1, . . . ,Fr ∈ Fr. We prove that for every p,μ ∈ (0,1) there exists r0 such that for all r > r0, all t with 1 ≤ t < (1/p− μ)r−1/(1− p)−1, there exist n0 and ε so that if n > n0 and |k/n− p|< ε , then |F1| · · · |Fr| ≤ (n−t k−t )r .
متن کاملA generalization of the Erdős-Ko-Rado Theorem
In this note, we investigate some properties of local Kneser graphs defined in [8]. In this regard, as a generalization of the Erdös-Ko-Rado theorem, we characterize the maximum independent sets of local Kneser graphs. Next, we present an upper bound for their chromatic number.
متن کاملOn the stability of the Erdős-Ko-Rado theorem
Delete the edges of a Kneser graph independently of each other with some probability: for what probabilities is the independence number of this random graph equal to the independence number of the Kneser graph itself? We prove a sharp threshold result for this question in certain regimes. Since an independent set in the Kneser graph is the same as a uniform intersecting family, this gives us a ...
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: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/707