Combinatorica

, Volume 16, Issue 3, pp 399–406 | Cite as

Norm-graphs and bipartite turán numbers

  • János Kollár
  • Lajos Rónyai
  • Tibor Szabó
Article

Abstract

For everyt>1 and positiven we construct explicit examples of graphsG with |V (G)|=n, |E(G)|≥c t ·n 2−1/t which do not contain a complete bipartite graghK t,t !+1 This establishes the exact order of magnitude of the Turán numbers ex (n, K t,s ) for any fixedt and allst!+1, improving over the previous probabilistic lower bounds for such pairs (t, s). The construction relies on elementary facts from commutative algebra.

Mathematics Subject Classification (1991)

05 C 35 14 A 25 

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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • János Kollár
    • 1
  • Lajos Rónyai
    • 2
  • Tibor Szabó
    • 3
    • 4
  1. 1.Department of MathematicsUniversity of UtahSalt Lake City
  2. 2.Computer and Automation InstituteHungarian Academy of SciencsHungary
  3. 3.Department of MathematicsThe Ohio State UniversityUSA
  4. 4.Eötvös Loránd UniversityBudapestHungary

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