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Combinatorica

, Volume 18, Issue 3, pp 373–404 | Cite as

Induced Ramsey Numbers

  • Y. Kohayakawa,
  • H. J. Prömel
  • V. Rödl
Original Paper

We investigate the induced Ramsey number\(\) of pairs of graphs (G, H). This number is defined to be the smallest possible order of a graph Γ with the property that, whenever its edges are coloured red and blue, either a red induced copy of G arises or else a blue induced copy of H arises. We show that, for any G and H with \(\), we have
$$$$
where \(\) is the chromatic number of H and C is some universal constant. Furthermore, we also investigate \(\) imposing some conditions on G. For instance, we prove a bound that is polynomial in both k and t in the case in which G is a tree. Our methods of proof employ certain random graphs based on projective planes.
AMS Subject Classification (1991) Classes:  05C55, 05C80; 05C35 

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Copyright information

© János Bolyai Mathematical Society, 1998

Authors and Affiliations

  • Y. Kohayakawa,
    • 1
  • H. J. Prömel
    • 2
  • V. Rödl
    • 3
  1. 1.Instituto de Matemática e Estatística, Universidade de São Paulo; Rua do Matão 1010, 05508–900 São Paulo, Brazil; E-mail: yoshi@ime.usp.brBR
  2. 2.Institut für Informatik, Humboldt-Universität zu Berlin; Unter den Linden 6, 10099 Berlin, Germany; E-mail: proemel@informatik.hu-berlin.deDE
  3. 3.Department of Mathematics and Computer Science, Emory University; Atlanta, GA 30322, USA; E-mail: rodl@mathcs.emory.eduUS

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