Combinatorica

, Volume 16, Issue 3, pp 399–406

Norm-graphs and bipartite turán numbers

  • János Kollár
  • Lajos Rónyai
  • Tibor Szabó
Article

DOI: 10.1007/BF01261323

Cite this article as:
Kollár, J., Rónyai, L. & Szabó, T. Combinatorica (1996) 16: 399. doi:10.1007/BF01261323

Abstract

For everyt>1 and positiven we construct explicit examples of graphsG with |V (G)|=n, |E(G)|≥ct·n2−1/t which do not contain a complete bipartite graghKt,t!+1 This establishes the exact order of magnitude of the Turán numbers ex (n, Kt,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 3514 A 25

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