More results on Ramsey—Turán type problems

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 .

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Erdős, P., Hajnal, A., Sós, V.T. et al. More results on Ramsey—Turán type problems. Combinatorica 3, 69–81 (1983). https://doi.org/10.1007/BF02579342

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AMS subject classification (1980)

  • 05 C 55
  • 05 C 35