Norm-graphs and bipartite Turán numbers

János Kollár, Lajos Rónyai, Tibor Szabó

Research output: Contribution to journalArticle

65 Citations (Scopus)


For every t > 1 and positive n we construct explicit examples of graphs G with |V(G)| = n, |E(G)| ≥ ct · n2-1/t which do not contain a complete bipartite graph Kt,t!+1. This establishes the exact order of magnitude of the Turán numbers ex(n,Kt,s) for any fixed t and all s ≥ t! + 1, improving over the previous probabilistic lower bounds for such pairs (t,s). The construction relies on elementary facts from commutative algebra.

Original languageEnglish
Pages (from-to)399-406
Number of pages8
Issue number3
Publication statusPublished - 1996

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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