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  • Combinatorics, Probability and Computing, Volume 5, Issue 1
  • March 1996, pp. 29-33

An Upper Bound on Zarankiewicz' Problem

  • Zoltán Füredi (a1)
  • DOI: http://dx.doi.org/10.1017/S0963548300001814
  • Published online: 01 September 2008
Abstract

Let ex(n, K3,3) denote the maximum number of edges of a K3,3-free graph on n vertices. Improving earlier results of Kővári, T. Sós and Turán on Zarankiewicz' problem, we obtain that Brown's example for a maximal K3,3-free graph is asymptotically optimal. Hence .

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[2]W. G. Brown (1966) On graphs that do not contain a Thomsen graph. Canad. Math. Bull. 9 (1966), 281289.

[6]P. Erdős and A. H. Stone (1946) On the structure of linear graphs. Bull. Amer. Math. Soc. 52, 10871091.

[7]Z. Füredi (1996) New asymptotics for bipartite Turän numbers. J. Combin. Th., Ser. A to appear.

[8]Z. Füredi (1996) On the number of edges of quadrilateral-free graphs. J. Combin. Th., Ser. B to appear.

[12]M. Mörs (1981) A new result on the problem of Zarankiewicz, J. Combin. Th., Ser. A31, 126130.

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