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

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.

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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.

  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.

  3. [3]

    P. Erdős, Problems and results on finite and infinite graphs, in:Recent advances in graph theory, Academia Praha (1975), 183–192.

  4. [4]

    J. Folkman, Graphs with monochromatic complete subgraphs in every edge coloring,SIAM J. Appl. Math. 18 (1970), 19–29.

    MATH  Article  MathSciNet  Google Scholar 

  5. [5]

    J. Nešetřil andV. Rödl, The Ramsey property for graphs with forbidden complete subgraphs,J. Comb. Theory B 20 (1976), 243–249.

    Article  Google 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.

    Article  Google 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.

    Article  MathSciNet  Google 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.

  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.

  10. [10]

    F. P. Ramsey, On a problem of formal logic,Proc. London Math. Soc. 30 (1930), 264–286.

    Article  Google Scholar 

  11. [11]

    V. Rödl, A generalization of Ramsey theorem, in:Graphs, Hypergraphs and Block Systems, Zielona Gora (1976), 211–220.

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Nešetřil, J., Rödl, V. Simple proof of the existence of restricted ramsey graphs by means of a partite construction. Combinatorica 1, 199–202 (1981). https://doi.org/10.1007/BF02579274

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AMS subject classification (1980)

  • 05 C 55