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An Upper Bound on Zarankiewicz' Problem

  • Zoltán Füredi (a1)
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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[1]Bollobás B. (1978) Extremal Graph Theory, Academic Press.
[2]Brown W. G. (1966) On graphs that do not contain a Thomsen graph. Canad. Math. Bull. 9 (1966), 281289.
[3]Erdős P. and Rényi A., (1960) On the evolution of random graphs. Magyar Tud. Akad. Mat. Kut. Int. Közl. 5, 1761. (Also see The Art of Counting, Selected Writings of P. Erdős, J. Spencer ed., pp. 574–617. MIT Press, 1973).
[4]Erdős P., Rényi A. and Sós V. T. (1966) On a problem of graph theory. Studia Sci. Math. Hungar. 1, 215235.
[5]Erdős P. and Simonovits M. (1966) A limit theorem in graph theory. Studia Sci. Math. Hungar. 1, 5157.
[6]Erdős P. and Stone A. H. (1946) On the structure of linear graphs. Bull. Amer. Math. Soc. 52, 10871091.
[7]Füredi Z. (1996) New asymptotics for bipartite Turän numbers. J. Combin. Th., Ser. A to appear.
[8]Füredi Z. (1996) On the number of edges of quadrilateral-free graphs. J. Combin. Th., Ser. B to appear.
[9]Hyltén-Cavallius C. (1958) On a combinatorial problem. Colloq. Math. 6, 5965.
[10]Kővári T., Sós V. T. and Turán P. (1954) On a problem of K. Zarankiewicz. Colloq. Math. 3, 5057.
[11]Mantel W. (1907) Problem 28. Wiskundige Opgaven 10 (1907), 6061.
[12]Mörs M. (1981) A new result on the problem of Zarankiewicz, J. Combin. Th., Ser. A 31, 126130.
[13]Turán P. (1941) On an extremal problem in graph theory, Mat. Fiz. Lapok 48, 436452 (in Hungarian). (Also see On the theory of graphs. Colloq. Math. 3, 19–30).
[14]Zarankiewicz K. (1951) Problem of P101, Colloq. Math. 2, 301.
[15]Znám Š. (1963) On a combinatorial problem of K. Zarankiewicz, Colloq. Math. 11, 8184. (Also see Two improvements of a result concerning a problem of K. Zarankiewicz. Colloq. Math. 13 (1965), 255–258).
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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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