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A simple proof of the Galvin-Ramsey property of the class of all finite graphs and a dimension of a graph. (English) Zbl 0388.05036


MSC:

05C55 Generalized Ramsey theory
05C35 Extremal problems in graph theory
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References:

[1] Graham, R. L.; Rothschild, B. L., Some recent developments in Ramsey theory, (Hall, M.; van Lint, J. H., Combinatorics (1975), D. Reidel Publ. Company: D. Reidel Publ. Company Dordrecht), 261-276 · Zbl 0303.05002
[2] Hales, A. W.; Jewett, R. I., Regularity and positional games, Trans. Amer. Math. Soc., 106, 222-229 (1963) · Zbl 0113.14802
[3] Colloquium on finite and infinite set theory, (Coll. Math. Soc. János Bolyai, 10 (1975), North-Holland: North-Holland Amsterdam)
[4] Nešetřil, J.; Rödl, V., A Ramsey graph without triangles exists for any graph without triangles, (Coll. Math. Soc. János Bolyai, 10 (1975), North-Holland: North-Holland Amsterdam), 1127-1132 · Zbl 0307.05127
[5] Nešetřil, J.; Rödl, V., Type theory of partition problems of graphs, (Fiedler, M., Recent Advances in Graph Theory (1975), Academia: Academia Prague), 405-412
[6] Nešeťril, J.; Rödl, V., Partitions of subgraphs, (Fiedler, M., Recent Advances in Graph Theory (1975), Academia: Academia Prague), 413-423
[7] Rado, R., Some combinatorial partition theorems, (Coll. Math. Soc. János Bolyai, 4 (1970), North-Holland: North-Holland Amsterdam) · Zbl 0216.29804
[8] Ramsey, F. P., On a problem of formal logic, Proc. London Math. Soc., 30, 2, 264-286 (1930) · JFM 55.0032.04
[9] Rödl, V., A generalization of Ramsey theorem, (Graphs, Hypergraphs and Block Systems (1976), Zielona: Zielona Gora), 211-220
[10] Sanders, J., A generalization of a theorem of Schur, (Doctoral Dissertation (1968), Yale: Yale New Haven, CT)
[11] Sabidussi, G., Subdirect representations of graphs (1975), Université de Montréal, preprint · Zbl 0308.05124
[12] Ore, O., Theory of graphs, Amer. Math. Soc. Colloq. Publ., XXVIII (1962)
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