Advertisement

Combinatorica

, Volume 1, Issue 2, pp 199–202 | Cite as

Simple proof of the existence of restricted ramsey graphs by means of a partite construction

  • Jaroslav Nešetřil
  • Vojtěch Rödl
Article

Abstract

By means of a partite construction we present a short proof of the Galvin Ramsey property of the class of all finite graphs and of its strengthening proved in [5]. We also establish a generalization of those results. Further we show that for every positive integerm there exists a graphH which is Ramsey forK m and does not contain two copies ofK m with more than two vertices in common.

AMS subject classification (1980)

05 C 55 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    W. Deuber, Generalizations of Ramsey’s theorem, in:Infinite and Finite Sets (A. Hajnal et al, eds.),Colloquia Mathematica Societatis J. Bolyai 10, North-Holland (1975), 323–332.Google Scholar
  2. [2]
    P. Erdős, A. Hajnal andL. Pósa, Strong embeddings of graphs into colored graphs, in:Infinite and finite sets (A. Hajnal et al., eds.)Coll. Math. Soc. J. Bolyai 10, North-Holland (1975), 1127–1132.Google Scholar
  3. [3]
    P. Erdős, Problems and results on finite and infinite graphs, in:Recent advances in graph theory, Academia Praha (1975), 183–192.Google Scholar
  4. [4]
    J. Folkman, Graphs with monochromatic complete subgraphs in every edge coloring,SIAM J. Appl. Math. 18 (1970), 19–29.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    J. Nešetřil andV. Rödl, The Ramsey property for graphs with forbidden complete subgraphs,J. Comb. Theory B 20 (1976), 243–249.CrossRefGoogle Scholar
  6. [6]
    J. Nešetřil andV. Rödl, A short constructive proof of the existence of highly chromatic graphs without short cycles,J. Comb. Theory B 27 (1979) 225–227.CrossRefGoogle Scholar
  7. [7]
    J. Nešetřil andV. Rödl, A simple proof of the Galvin Ramsey property of the class of all finite graphs and a dimension of a graph,Discrete Mathematics 23 (1978), 49–55.CrossRefMathSciNetGoogle Scholar
  8. [8]
    J. Nešetřil andV. Rödl, Partition (Ramsey) theory — a survey, in:Combinatorics (A. Hajnal and Vera T. Sós, eds.)Coll. Math. Soc. J. Bolyai 18, North-Holland (1978), 759–792.Google Scholar
  9. [9]
    J. Nešetřil andV. Rödl, Partition theory and its application, in:Surveys in Combinatorics, (B. Bollobás, ed.)London Math. Soc. Lecture Notes 38, Cambridge Univ. Press 1979, 96–156.Google Scholar
  10. [10]
    F. P. Ramsey, On a problem of formal logic,Proc. London Math. Soc. 30 (1930), 264–286.CrossRefGoogle Scholar
  11. [11]
    V. Rödl, A generalization of Ramsey theorem, in:Graphs, Hypergraphs and Block Systems, Zielona Gora (1976), 211–220.Google Scholar

Copyright information

© Akadémiai Kiadó 1981

Authors and Affiliations

  • Jaroslav Nešetřil
    • 1
  • Vojtěch Rödl
    • 2
  1. 1.KZAA MFF KU, Charles UniversityPraha 8Czechoslovakia
  2. 2.KM FJFI CVUT, Czech Technical Univ.Praha 1Czechoslovakia

Personalised recommendations