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    Blagojević, Pavle V. M. Bukh, Boris and Karasev, Roman 2013. Turán numbers for K s,t -free graphs: Topological obstructions and algebraic constructions. Israel Journal of Mathematics, Vol. 197, Issue. 1, p. 199.
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Asymptotic Improvements to the Lower Bound of Certain Bipartite Turán Numbers

  • SIMEON BALL (a1) and VALENTINA PEPE (a2)
Abstract

We show that there are graphs with n vertices containing no K5,5 which have about n7/4 edges, thus proving that ex(n, K5,5) ≥ (1 + o(1))n7/4. This bound gives an asymptotic improvement to the known lower bounds on ex(n, Kt, s) for t = 5 when 5 ≤ s ≤ 12, and t = 6 when 6 ≤ s ≤ 8.

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COPYRIGHT: © Cambridge University Press 2011
References
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[1]Alon, N., Rónyai, L. and Szabó, T. (1999) Norm-graphs: Variations and applications. J. Combin. Theory Ser. B 76 280–290.
[2]Bohman, T. and Keevash, P. (2010) The early evolution of the H-free process. Invent. Math. 181 291–336.
[3]Bollobás, B. (1978) Extremal Graph Theory, Academic Press.
[4]Brown, W. G. (1966) On graphs that do not contain a Thomsen graph. Canad. Math. Bull. 9 281–289.
[5]Erdős, P., Rényi, A. and Sós, V. T. (1966) On a problem of graph theory. Studia Sci. Math. Hungar. 1 215–235.
[6]Erdős, P. and Spencer, J. (1974) Probabilistic Methods in Combinatorics, Academic Press/Akadémiai Kiadó.
[7]Erdős, P. and Stone, A. H. (1946) On the structure of linear graphs. Bull. Amer. Math. Soc. 52 1087–1091.
[8]Füredi, Z. (1996) An upper bound on Zarankiewicz' problem. Combin. Probab. Comput. 5 29–33.
[9]Füredi, Z. (1996) New asymptotics for bipartite Turán numbers. J. Combin. Theory Ser. A 75 141–144.
[10]Kővári, T., Sós, V. T. and Turán, P. (1954) On a problem of K. Zarankiewicz. Colloq. Math. 3 50–57.
[11]Pepe, V. (2011) On the algebraic variety r, t. Finite Fields Appl. 17 343–349.
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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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