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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.
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.