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Asymptotic Improvements to the Lower Bound of Certain Bipartite Turán Numbers

Published online by Cambridge University Press:  03 October 2011

SIMEON BALL  and
VALENTINA PEPE
SIMEON BALL
Affiliation:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Jordi Girona 1–3, Mòdul C3, Campus Nord, 08034 Barcelona, Spain (e-mail: simeon@ma4.upc.edu)
VALENTINA PEPE
Affiliation:
Department of Mathematics, Ghent University, Krijgslaan 281, Building S22, 9000 Gent, Belgium (e-mail: valepepe@cage.ugent.be)
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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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 3 , May 2012 , pp. 323 - 329
Copyright
Copyright © Cambridge University Press 2011

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