A generalization of the Erdös-Ko-Rado theorem on finite set systems
Andras Hajnal,Bruce Rothschild +1 more
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A family T of k-subsets of an n-set such that no more than r have pairwise fewer than s elements in common is maximum (for sufficiently large n) only if T consists of all the k-sets containing at least one of r fixed disjoint s- Subsets.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-11-01 and is currently open access. It has received 34 citations till now. The article focuses on the topics: Disjoint sets & Generalization.read more
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Erdös–Ko–Rado Theorem—22 Years Later
Michel Deza,Peter Frankl +1 more
TL;DR: A survey of known and of some new generalizations and analogues of Erdos, Ko, and Rado's theorem can be found in this article, where the authors consider mostly problems which were not included or were touched very briefly in the survey papers [17], [46], [51], [61].
Journal ArticleDOI
The chromatic number of kneser hypergraphs
TL;DR: In this article, Barany, Shlosman and Szucs utilise a conjecture d'Erlos relative a la coloration des r-sousensembles d'un ensemble a n elements and un theoreme de partition optimale.
Book ChapterDOI
Extremal Problems for Hypergraphs
TL;DR: In this article, a hypergraph is defined as a pair (V,A) where V is a finite set, and A = {A1,…,Am} is a family of its different subsets.
Journal ArticleDOI
Intersection properties of systems of finite sets
TL;DR: In this paper, a finite set of cardinality n is defined as a set of nonnegative integers with 11 enr-1 (c = e(k) is a constant depending on k).
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Extremal problems concerning Kneser graphs
Peter Frankl,Zoltán Füredi +1 more
TL;DR: It is proven that equality holds for n> 1 2 (3+ 5 )k , and equality holds only if there exist two points a, b such that {a, b} ∩ F ≠ ∅ for all F ∈ A ∪ B.
References
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Intersection theorems for systems of finite sets
Paul Erdös,Chao Ko,Richard Rado +2 more
TL;DR: In this article, the obliteration operator is used to remove from any system of elements the element above which it is placed, and the set of all systems (ao,av...,dn) such that avc[0,m); \av\ 1 (v < »),