Norm-graphs and bipartite turán numbers

Combinatorica volume 16, pages399–406(1996)Cite this 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 alls≥t!+1, improving over the previous probabilistic lower bounds for such pairs (t, s). The construction relies on elementary facts from commutative algebra.

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Author information

Affiliations

  1. Department of Mathematics, University of Utah, 84112, Salt Lake City, UT

    János Kollár

  2. Computer and Automation Institute, Hungarian Academy of Sciencs, Hungary

    Lajos Rónyai

  3. Department of Mathematics, The Ohio State University, Ohio, USA

    Tibor Szabó

  4. Eötvös Loránd University, Budapest, Hungary

    Tibor Szabó

Authors
  1. János Kollár
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  2. Lajos Rónyai
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  3. Tibor Szabó
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Additional information

Research supported in part by NSF Grants DMS-8707320 and DMS-9102866.

Research supported in part by Hungarian National Foundation for Scientific Research Grant

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Kollár, J., Rónyai, L. & Szabó, T. Norm-graphs and bipartite turán numbers. Combinatorica 16, 399–406 (1996). https://doi.org/10.1007/BF01261323

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Mathematics Subject Classification (1991)

  • 05 C 35
  • 14 A 25