Abstract
Many papers and also the excellent book of Bollobás, recently appeared on extremal problems on graphs. Two survey papers of Simonovits are in the press and Brown, Simonovits and I have several papers, some appeared, some in the press and some in preparation on this subject.
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References
Ajtai, M., Komlos, J., Szemerédi, E. (1981): A dense infinite Sidon sequence. Eur. J. Comb. 2, 1–11
Beck, J., Csirmaz, L. (1982): Variations on a game. J. Comb. Theory, Ser. A 33, 297–315
Bollobás, B. (1974): Three graphs without two triples whose symmetric difference is contained in a third. Discrete Math. 8, 21–24
Bollobás, B., Erdös, P., Simonovits, M., Szemerédi, E. (1978): External graphs without large forbidden subgraphs. In: Bollobás, B. (ed.): Advances in graph theory. North Holland, Amsterdam, pp. 29–41 (Ann. Discrete Math., Vol. 3)
Brown, W.G., Erdôs, P., Simonovits, M. (1973): Extremal problems for directed graphs. J. Comb. Theory, Ser. B 15, 77–93 [Several further papers of ours will appear in the near or distant future (I omit the usual “if we live” since the papers are more or less in their final form). For a preliminary account see Brown, W.G., Erdôs, P., Simonovits, M. (1978): On multigraph extremal problems. In: Bermond, J.-C., Fournier, J.-C., Las Vergnas, M., Sotteau, D. (eds): Problèmes combinatoires et théorie des graphes. Centre National de la Recherche Scientifique, Paris, pp. 63–66 (Colloq. Int. CNRS, Vol. 260)]
Brown, WG., Erdös, P., Sós, V. (1973): Some extremal problems on r-graphs. In: Harary, F. (ed.): New directions in the theory of graphs. Academic Press, New York, NY, pp. 53–63
Brown, W.G., Sos, V., Erdôs, P. (1973): On the existence of triangulated spheres in 3-graphs, and related problems. Period. Math. Hung. 3, 221–228
Erdös, P . (1961): Graph theory and probability II. Can. J. Math. 13, 346–352 [See also Erdös, P. (1973): The art of counting: selected writings. MIT Press, Cambridge, MA, pp. 411–417 (Math. Time, Vol. 5)]
Erdös, P. (1965): On extremal problems of graphs and generalized graphs. Isr. J. Math. 2, 189–190
Erdös, P. (1977): Problems and results in combinatorial analysis. In: Hoffman, F., Lesniak-Foster, L., McCarthy, D., Mullin, R.C., Reid, K.B., Stanton, R.G. (eds.): Proc. 8th Southeastern Conference on Combinatorics, Graph Theory and Computing. Utilitas Mathematica, Winnipeg, pp. 3–12 (Congr. Numerantium, No. XIX)
Erdös, P., Hajnal, A. (1972): On Ramsey like theorems. Problems and results. In: Welsh, D.J.A., Woodall, D.R. (eds.): Combinatorics. Institute of Mathematics and its Applications, Southend-on-Sea, pp. 123–140
Erdös, P., Simonovits, M. (1970): Some extremal problems in graph theory. In: Erdös, P., Rényi, A., Sós, V. (eds.): Combinatorial theory and its applications I. North Holland, Amsterdam, pp. 377–390 (Colloq. Math. Soc. János Bolyai, Vol. 4)
Erdös, P., Sos, V. (1982): On Ramsey-Turan type theorems for hypergraphs. Combinatorica 2, 289–295 [This paper contains many unsolved problems and also has references to the older literature]
Erdös, P., Spencer, J. (1974): Probabilistic methods in combinatorics. Academic Press, New York, NY (Probab. Math. Stat., Vol. 17)
Erdös, P., Stone, A. (1946): On the structure of linear graphs. Bull. Am. Math. Soc. 52, 1087–1091
Erdös, P., Hajnal, A., Rado, R. (1965): Partition relations for cardinal numbers. Acta Math. Acad. Sci. Hung. 16, 93–196
Erdös, P., Hajnal, A., Sos, V., Szemeredi, E. (1983): More results on Ramsey-Turan type problems. Combinatorica 5, 69–81 [This paper contains references to the older papers]
Frankl, P., Füredi, Z. (1983): A new generalization of the Erdos-Ko-Rado theorem. Combinatorica 3, 341–349
Frankl, P., Rödl, V. (1984): Hypergraphs do not jump. Combinatorica 4, 149–160
Frankl, P., Rödl, V.: Ramsey-Turan theorems for hypergraphs. Submitted to Combinatorica
Graver, J.E., Yackel, J. (1968): Some graph theoretic results associated with Ramsey’s theorem. J. Comb. Theory 4, 125–175
Komlós, J., Pintz, J., Szemeredi, E. (1981): On Heilbronn’s triangle problem. J. Lond. Math. Soc., II. Ser. 24, 385–396
Komlós, J., Pintz, J., Szemeredi, E. (1982): A lower bound for Heilbronn’s problem. J. Lond. Math. Soc., II. Ser. 25, 13–24
Rödl, V.: Note on a Ramsey-Turan type problem.
Ruzsa, IZ., Szemerédi, E. (1978): Triple systems with no six points carrying three triangles. In: Hajnal, A., Sós, V. (eds.): Combinatorics II. North Holland, Amsterdam, pp. 939–945 (Colloq. Math. Soc. János Bolyai, Vol. 18)
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Erdös, P. (1990). Problems and Results on Graphs and Hypergraphs: Similarities and Differences. In: Nešetřil, J., Rödl, V. (eds) Mathematics of Ramsey Theory. Algorithms and Combinatorics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72905-8_2
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