Ramsey-Turán theory

Miklós Simonovits, Vera T. Sós

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Ramsey- and Turán-type problems were always strongly related to each other. Motivated by an observation of Paul Erdos, it was Turán who started the systematic investigation of the applications of extremal graph theory in geometry and analysis. This led the second author to some results and problems which, in turn, led to the birth of Ramsey-Turán-type theorems. Today this is a wide field of research with many interesting results and many unsolved problems. Below we give a short survey of the most important parts of this field: starting with a historical sketch we continue by describing the • Ramsey-Turán-type problems and results. • Related problems in Ramsey theory. • Some applications.

Original languageEnglish
Pages (from-to)293-340
Number of pages48
JournalDiscrete Mathematics
Volume229
Issue number1-3
DOIs
Publication statusPublished - Feb 28 2001

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Keywords

  • Geometry
  • Graphs
  • Hypergraphs
  • Ramsey theory
  • Ramsey-Turán theorems
  • Turán-type extremal graph theory

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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