On Ramsey-Turán type theorems for hypergraphs

P. Erdős, Vera T. Sós

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

Let H r be an r-uniform hypergraph. Let g=g(n;H r ) be the minimal integer so that any r-uniform hypergraph on n vertices and more than g edges contains a subgraph isomorphic to H r . Let e =f(n;H r, εn) denote the minimal integer such that every r-uniform hypergraph on n vertices with more than e edges and with no independent set of εn vertices contains a subgraph isomorphic to H r . We show that if r>2 and H r is e.g. a complete graph then {Mathematical expression} while for some H r with {Mathematical expression} {Mathematical expression}. This is in strong contrast with the situation in case r=2. Some other theorems and many unsolved problems are stated.

Original languageEnglish
Pages (from-to)289-295
Number of pages7
JournalCombinatorica
Volume2
Issue number3
DOIs
Publication statusPublished - Sep 1982

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Uniform Hypergraph
Hypergraph
Subgraph
Isomorphic
Theorem
Integer
Independent Set
Complete Graph
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Keywords

  • AMS subject classification (1980): 05C65, 05C35, 05C55

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

On Ramsey-Turán type theorems for hypergraphs. / Erdős, P.; Sós, Vera T.

In: Combinatorica, Vol. 2, No. 3, 09.1982, p. 289-295.

Research output: Contribution to journalArticle

Erdős, P. ; Sós, Vera T. / On Ramsey-Turán type theorems for hypergraphs. In: Combinatorica. 1982 ; Vol. 2, No. 3. pp. 289-295.
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