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Graphs and Combinatorics

, Volume 1, Issue 1, pp 213–216 | Cite as

Lower bounds for Turán's problem

  • Peter Frankl
  • Vojtěch Rödl
Article

Abstract

Turán's problem is to determine the maximum numberT(n,k,t) oft-element subsets of ann-set without a complete sub-hypergraph onk vertices, i.e., allt-subsets of ak-set. It is proved that fora≥1 fixed andt sufficiently largeT(n, t+a,t)>(1-a(a+4+o(1))logt/( a t )( t n holds

Keywords

Positive Integer Lower Bound Extremal Problem Pure Mathematic Present Note 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    de Caen, D.: Extension of a theorem of Moon and Moser on complete subgraphs. Ars Comb.16, 5–10 (1983)zbMATHGoogle Scholar
  2. 2.
    Erdös, P., Lovász, L.: On 3-chromatic hypergraphs. Infinite and finite sets. Colloq. Math. Soc. János Bolyai10, 609–627 (1975)Google Scholar
  3. 3.
    Katona, G.O.H., Nemetz, T., Simonovits, M.: On a graph-problem of Turán (in Hungarian). Mat. Lapok15, 228–238 (1964)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Kim, H.K., Roush, F.W.: On a problem of Turán. In: Studies in Pure Mathematics, pp. 423–425. Basel: Birkhäuser 1983Google Scholar
  5. 5.
    Tazawa, S.: Lecture delivered at Japan Math. Soc. Meeting, April 1983Google Scholar
  6. 6.
    Turán, P.: An extremal problem in graph theory (in Hungarian). Mat. Fiz. Lapok48, 436–452 (1941)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Peter Frankl
    • 1
  • Vojtěch Rödl
    • 2
  1. 1.CNRSParisFrance
  2. 2.FJFI, CVUTprague 1Czechoslovakia

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