Simple proof of the existence of restricted ramsey graphs by means of a partite construction
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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 . 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
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- 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
- 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
- P. Erdős, Problems and results on finite and infinite graphs, in:Recent advances in graph theory, Academia Praha (1975), 183–192.Google Scholar
- 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
- 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
- V. Rödl, A generalization of Ramsey theorem, in:Graphs, Hypergraphs and Block Systems, Zielona Gora (1976), 211–220.Google Scholar