A note on G-intersecting families
نویسندگان
چکیده
منابع مشابه
G-Intersecting Families
Let G be a graph on vertex set [n], and for X [n] let N(X) be the union of X and it's neighborhood in G. A family of sets F 2 is G-intersecting if N(X) \ Y 6= ; for all X;Y 2 F . In this paper we study the cardinality and structure of the largest k-uniform G-intersecting families on a xed graph G.
متن کاملOn Symmetric Intersecting Families
A family of sets is said to be symmetric if its automorphism group is transitive, and intersecting if any two sets in the family have nonempty intersection. Our purpose here is to study the following question: for n, k ∈ N with k ≤ n/2, how large can a symmetric intersecting family of k-element subsets of {1, 2, . . . , n} be? As a first step towards a complete answer, we prove that such a fami...
متن کاملOn cross-intersecting families
Frankl, P., On cross-intersecting families, Discrete Mathematics 108 (1992) 291-295. Let n 3 t z 1 be integers. Let 9, YI be families of subsets of the n-element set X. They are called cross t-intersecting if IF n GI 2 t holds for all F E 9 and G E 3. If 9 = CfI then 9 is called t-intersecting. Let m(n, t) denote the maximum possible cardinality of a r-intersecting family. Our main result says ...
متن کاملA note on Huang-Zhao theorem on intersecting families with large minimum degree
Using the linear algebra method Huang and Zhao proved that if n > 2k and F is an intersecting n-vertex k-uniform hypergraph with minimum degree at least ( n−2 k−2 ) , then F is the star. In this note we present an elementary, combinatorial proof of this result for the case n ≥ 3k. We also prove a vector space version of the Huang–Zhao result along the same line as their proof.
متن کاملFamilies intersecting on an interval
We shall be interested in the following Erdős-Ko-Rado-type question. Fix some set B ⊂ [n]. How large a family A ⊂ P [n] can we find such that the intersection of any two sets in A contains a cyclic translate (modulo n) of B? Chung, Graham, Frankl and Shearer have proved that, in the case where B is a block of length t, we can do no better than to take A to consist of all supersets of B. We give...
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: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00761-6