Exact solution of some Turán-type problems
type: Item
instance of: scholarly article
title: Exact solution of some Turán-type problems
zbMATH Open document ID: 0661.05003
DOI: 10.1016/0097-3165(87)90016-1
published in: Journal of Combinatorial Theory. Series A
publication date: 1987-01-01T00:00:00Z
review text: Fifteen years ago Chvátal conjectued that if \({\mathcal F}\) is a family of k subsets of an n-set, \(| {\mathcal F}| >\left( \begin{matrix} n-1\\ k- 1\end{matrix} \right)\), d is an arbitrary integer with \(d\leq k-1\) and \((d+1)k\leq dn\), then there exist \(d+1\) sets in \({\mathcal F}\) with empty intersection such that the intersection of any d of them is non-empty. The validity of this conjecture is established for \(n\geq n_ 0(k)\), in a more general framework. Another problem which is solved asymptotically is when the excluded configuration is a fixed sunflower.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 4079427
zbMATH Keywords: family of subsets
zbMATH Keywords: empty intersection
zbMATH Keywords: excluded configuration
zbMATH Keywords: fixed sunflower
author: Peter Frankl
author: Zoltán Füredi
MaRDI profile type: Publication
full work available at URL: 0097-3165(87)90016-1
OpenAlex ID: W2100896331
cites work: Intersection theorems for systems of sets
cites work: On a Conjecture of Chvátal on m -Intersecting Hypergraphs
cites work: On generalized graphs
cites work: Three-graphs without two triples whose symmetric difference is contained in a third
cites work: Q3852212
cites work: On the existence of triangulated spheres in 3-graphs, and related problems
cites work: Q5672676
cites work: Q3313888
cites work: The maximum number of edges in a 3-graph not containing a given star
cites work: An Extremal Set-Intersection Theorem
cites work: Intersection Properties of Systems of Finite Sets
cites work: Q3885763
cites work: On extremal problems of graphs and generalized graphs
cites work: Q5510578
cites work: Q4777298
cites work: Q4101818
cites work: On the combinatorial problems which I would most like to see solved
cites work: Q5543308
cites work: INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
cites work: Intersection Theorems for Systems of Sets
cites work: Supersaturated graphs and hypergraphs
cites work: On Sperner families satisfying an additional condition
cites work: Q4184835
cites work: A General Intersection Theorem For Finite Sets
cites work: On a problem of Chvatal and Erdoes on hypergraphs containing no generalized simplex
cites work: A new short proof for the Kruskal-Katona theorem
cites work: Q3772225
cites work: A new generalization of the Erdős-Ko-Rado theorem
cites work: An exact result for 3-graphs
cites work: Forbidding just one intersection
cites work: Q3941411
cites work: Lower bounds for Turán's problem
cites work: Linear dependencies among subsets of a finite set
cites work: Intersection theorems with geometric consequences
cites work: On finite set-systems whose every intersection is a kernel of a star
cites work: Graphs without quadrilaterals
cites work: A new approach to Turán's conjecture
cites work: Extremal problems for finite sets and convex hulls---a survey
cites work: Q4052170
cites work: Q5512796
cites work: Q5726070
cites work: A note on the realization of distances within sets in euclidean space
cites work: Q3880849
cites work: Q3758729
cites work: On a packing and covering problem
cites work: Q4175585
cites work: Q4133991
cites work: Q5781249
cites work: The exact bound in the Erdős-Ko-Rado theorem
description: scientific article; zbMATH DE number 4079427