Corpus ID: 220793154

Some remarks on the Zarankiewicz problem

  title={Some remarks on the Zarankiewicz problem},
  author={D. Conlon},
  journal={arXiv: Combinatorics},
  • D. Conlon
  • Published 2020
  • Mathematics
  • arXiv: Combinatorics
  • The Zarankiewicz problem asks for an estimate on z(m,n;s,t), the largest number of 1's in an m×n matrix with all entries 0 or 1 containing no s×t submatrix consisting entirely of 1's. We show that a classical upper bound for z(m,n;s,t) due to Kővari, Sos and Turan is tight up to the constant for a broad range of parameters. The proof relies on a new quantitative variant of the random algebraic method. 


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