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Problems and Results on Graphs and Hypergraphs: Similarities and Differences

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Mathematics of Ramsey Theory

Part of the book series: Algorithms and Combinatorics ((AC,volume 5))

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

    MATH  Google Scholar 

  • Beck, J., Csirmaz, L. (1982): Variations on a game. J. Comb. Theory, Ser. A 33, 297–315

    Article  MathSciNet  Google Scholar 

  • Bollobás, B. (1974): Three graphs without two triples whose symmetric difference is contained in a third. Discrete Math. 8, 21–24

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Chapter  Google Scholar 

  • 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)]

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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)]

    Article  MATH  Google Scholar 

  • Erdös, P. (1965): On extremal problems of graphs and generalized graphs. Isr. J. Math. 2, 189–190

    Google Scholar 

  • 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)

    Google Scholar 

  • 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

    Google Scholar 

  • 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)

    Google Scholar 

  • 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]

    Article  MathSciNet  MATH  Google Scholar 

  • Erdös, P., Spencer, J. (1974): Probabilistic methods in combinatorics. Academic Press, New York, NY (Probab. Math. Stat., Vol. 17)

    MATH  Google Scholar 

  • Erdös, P., Stone, A. (1946): On the structure of linear graphs. Bull. Am. Math. Soc. 52, 1087–1091

    Article  MATH  Google Scholar 

  • Erdös, P., Hajnal, A., Rado, R. (1965): Partition relations for cardinal numbers. Acta Math. Acad. Sci. Hung. 16, 93–196

    Article  MATH  Google Scholar 

  • 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]

    Article  Google Scholar 

  • Frankl, P., Füredi, Z. (1983): A new generalization of the Erdos-Ko-Rado theorem. Combinatorica 3, 341–349

    Article  MathSciNet  MATH  Google Scholar 

  • Frankl, P., Rödl, V. (1984): Hypergraphs do not jump. Combinatorica 4, 149–160

    Article  MathSciNet  MATH  Google Scholar 

  • Frankl, P., Rödl, V.: Ramsey-Turan theorems for hypergraphs. Submitted to Combinatorica

    Google Scholar 

  • Graver, J.E., Yackel, J. (1968): Some graph theoretic results associated with Ramsey’s theorem. J. Comb. Theory 4, 125–175

    Article  MathSciNet  MATH  Google Scholar 

  • Komlós, J., Pintz, J., Szemeredi, E. (1981): On Heilbronn’s triangle problem. J. Lond. Math. Soc., II. Ser. 24, 385–396

    Article  MATH  Google Scholar 

  • Komlós, J., Pintz, J., Szemeredi, E. (1982): A lower bound for Heilbronn’s problem. J. Lond. Math. Soc., II. Ser. 25, 13–24

    Article  MATH  Google Scholar 

  • Rödl, V.: Note on a Ramsey-Turan type problem.

    Google Scholar 

  • 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)

    Google Scholar 

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© 1990 Springer-Verlag Berlin Heidelberg

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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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  • DOI: https://doi.org/10.1007/978-3-642-72905-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-72907-2

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