Results 1  10
of
287
Uniformly cross intersecting families
, 2006
"... Let A and B denote two families of subsets of an nelement set. The pair (A, B) is said to be ℓcrossintersecting iff A∩B  = ℓ for all A ∈ A and B ∈ B. Denote by Pℓ(n) the maximum value of AB  over all such pairs. The best known upper bound on Pℓ(n) is Θ(2n), by Frankl and Rödl. For a lower ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Let A and B denote two families of subsets of an nelement set. The pair (A, B) is said to be ℓcrossintersecting iff A∩B  = ℓ for all A ∈ A and B ∈ B. Denote by Pℓ(n) the maximum value of AB  over all such pairs. The best known upper bound on Pℓ(n) is Θ(2n), by Frankl and Rödl. For a lower
Intersecting families — uniform versus weighted
 Ryukyu Math. J
"... ABSTRACT. What is the maximal size of kuniform rwise tintersecting families? We show that this problem is essentially equivalent to determine the maximal weight of nonuniform rwise tintersecting families. Some EKR type examples and their applications are included. 1. ..."
Abstract

Cited by 9 (8 self)
 Add to MetaCart
ABSTRACT. What is the maximal size of kuniform rwise tintersecting families? We show that this problem is essentially equivalent to determine the maximal weight of nonuniform rwise tintersecting families. Some EKR type examples and their applications are included. 1.
Uniform Intersecting Families With Covering Number Restrictions
 Tracts in Theoretical Computer Science 7
, 1994
"... It is known that any kuniform family with covering number t has at most k t tcovers. In this paper, we give better upper bounds for the number of tcovers in kuniform intersecting families with covering number t. 1 ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
It is known that any kuniform family with covering number t has at most k t tcovers. In this paper, we give better upper bounds for the number of tcovers in kuniform intersecting families with covering number t. 1
Isomorphism Classes of Maximal Intersecting Uniform Families Are Few
"... Denote by f(k, m) the number of isomorphism classes of maximal intersecting kuniform 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. 1 ..."
Abstract
 Add to MetaCart
Denote by f(k, m) the number of isomorphism classes of maximal intersecting kuniform 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. 1
Triangleintersecting Families of Graphs
, 2010
"... A family of graphs F is triangleintersecting if for every G, H ∈ F, G∩H contains a triangle. A conjecture of Simonovits and Sós from 1976 states that the largest triangleintersecting families of graphs on a fixed set of n vertices are those obtained by fixing a specific triangle and taking all gra ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
graphs containing it, resulting in a family of size 1 82(n2). We prove this conjecture and some generalizations (for example, we prove that the same is true of oddcycleintersecting families, and we obtain best possible bounds on the size of the family under different, not necessarily uniform, measures
Nontrivial intersecting uniform subfamilies of hereditary families
"... Abstract For a family F of sets, let µ(F) denote the size of a smallest set in F that is not a subset of any other set in F, and for any positive integer r, let F (r) denote the family of relement sets in F. We say that a family A is of HiltonMilner (HM ) type if for some A ∈ A, all sets in A\{A} ..."
Abstract
 Add to MetaCart
\{A} have a common element x / ∈ A and intersect A. We show that if a hereditary family H is compressed and µ(H) ≥ 2r ≥ 4, then the HMtype family {A ∈ H (r) : 1 ∈ A, A ∩ [2, r + 1] = ∅} ∪ {[2, r + 1]} is a largest nontrivial intersecting subfamily of H (r) ; this generalises a wellknown result of Hilton
Gintersecting Families
, 1999
"... Let G be a graph on vertex set [.], and for X C_ [.] let N(X) be the union of X and it's neighborhood in G. A family of sets ' C 2 ["] is Gintersectin# if N(X) Y 0 for all X, Y '. In this paper we study the cardinality and structure of the largest kuniform Gintersecting fa ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Let G be a graph on vertex set [.], and for X C_ [.] let N(X) be the union of X and it's neighborhood in G. A family of sets ' C 2 ["] is Gintersectin# if N(X) Y 0 for all X, Y '. In this paper we study the cardinality and structure of the largest kuniform Gintersecting
Covers in uniform intersecting families and a counterexample to a conjecture of Lovász
 J. Comb. Theory (A
, 1992
"... We discuss the maximum size of uniform intersecting families with covering number at least . Among others, we construct a large kuniform 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 a ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We discuss the maximum size of uniform intersecting families with covering number at least . Among others, we construct a large kuniform 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 the number of maximal intersecting kuniform families and further applications of . . .
, 2015
"... ..."
ON CROSS tINTERSECTING FAMILIES OF SETS
, 2010
"... For all p,t with 0 < p < 0.11 and 1 ≤ t ≤ 1/(2p), there exists n0 such that for all n,k with n> n0 and k/n = p the following holds: if A and B are kuniform families on n vertices, and A ∩ B  ≥ t holds for all A ∈ A and B ∈ B, then A B  ≤ ( n−t) 2. k−t 1. ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
For all p,t with 0 < p < 0.11 and 1 ≤ t ≤ 1/(2p), there exists n0 such that for all n,k with n> n0 and k/n = p the following holds: if A and B are kuniform families on n vertices, and A ∩ B  ≥ t holds for all A ∈ A and B ∈ B, then A B  ≤ ( n−t) 2. k−t 1.
Results 1  10
of
287