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Combinatorica

, Volume 3, Issue 1, pp 69–81 | Cite as

More results on Ramsey—Turán type problems

  • P. Erdős
  • A. Hajnal
  • Vera T. Sós
  • E. Szemerédi
Article

Abstract

The paper deals with common generalizations of classical results of Ramsey and Turán. The following is one of the main results. Assumek≧2, ε>0,G n is a sequence of graphs ofn-vertices and at least 1/2((3k−5) / (3k−2)+ε)n 2 edges, and the size of the largest independent set inG n iso(n). LetH be any graph of arboricity at mostk. Then there exists ann 0 such that allG n withn>n 0 contain a copy ofH. This result is best possible in caseH=K 2k .

AMS subject classification (1980)

05 C 55 05 C 35 

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Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • P. Erdős
    • 1
  • A. Hajnal
    • 1
  • Vera T. Sós
    • 1
  • E. Szemerédi
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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