Problems and Results on Graphs and Hypergraphs: Similarities and Differences

  • Paul Erdös
Part of the Algorithms and Combinatorics book series (AC, volume 5)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ajtai, M., Komlos, J., Szemerédi, E. (1981): A dense infinite Sidon sequence. Eur. J. Comb. 2, 1–11zbMATHGoogle Scholar
  2. Beck, J., Csirmaz, L. (1982): Variations on a game. J. Comb. Theory, Ser. A 33, 297–315MathSciNetCrossRefGoogle Scholar
  3. Bollobás, B. (1974): Three graphs without two triples whose symmetric difference is contained in a third. Discrete Math. 8, 21–24MathSciNetCrossRefzbMATHGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 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)]CrossRefGoogle Scholar
  6. 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. 53–63Google Scholar
  7. Brown, W.G., Sos, V., Erdôs, P. (1973): On the existence of triangulated spheres in 3-graphs, and related problems. Period. Math. Hung. 3, 221–228CrossRefzbMATHGoogle Scholar
  8. 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)]CrossRefzbMATHGoogle Scholar
  9. Erdös, P. (1965): On extremal problems of graphs and generalized graphs. Isr. J. Math. 2, 189–190Google Scholar
  10. 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
  11. 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. 123–140Google Scholar
  12. 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
  13. 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]MathSciNetCrossRefzbMATHGoogle Scholar
  14. Erdös, P., Spencer, J. (1974): Probabilistic methods in combinatorics. Academic Press, New York, NY (Probab. Math. Stat., Vol. 17)zbMATHGoogle Scholar
  15. Erdös, P., Stone, A. (1946): On the structure of linear graphs. Bull. Am. Math. Soc. 52, 1087–1091CrossRefzbMATHGoogle Scholar
  16. Erdös, P., Hajnal, A., Rado, R. (1965): Partition relations for cardinal numbers. Acta Math. Acad. Sci. Hung. 16, 93–196CrossRefzbMATHGoogle Scholar
  17. 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]CrossRefGoogle Scholar
  18. Frankl, P., Füredi, Z. (1983): A new generalization of the Erdos-Ko-Rado theorem. Combinatorica 3, 341–349MathSciNetCrossRefzbMATHGoogle Scholar
  19. Frankl, P., Rödl, V. (1984): Hypergraphs do not jump. Combinatorica 4, 149–160MathSciNetCrossRefzbMATHGoogle Scholar
  20. Frankl, P., Rödl, V.: Ramsey-Turan theorems for hypergraphs. Submitted to CombinatoricaGoogle Scholar
  21. Graver, J.E., Yackel, J. (1968): Some graph theoretic results associated with Ramsey’s theorem. J. Comb. Theory 4, 125–175MathSciNetCrossRefzbMATHGoogle Scholar
  22. Komlós, J., Pintz, J., Szemeredi, E. (1981): On Heilbronn’s triangle problem. J. Lond. Math. Soc., II. Ser. 24, 385–396CrossRefzbMATHGoogle Scholar
  23. Komlós, J., Pintz, J., Szemeredi, E. (1982): A lower bound for Heilbronn’s problem. J. Lond. Math. Soc., II. Ser. 25, 13–24CrossRefzbMATHGoogle Scholar
  24. Rödl, V.: Note on a Ramsey-Turan type problem.Google Scholar
  25. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Paul Erdös

There are no affiliations available

Personalised recommendations