“…Füredi [15] obtained (1.7) and Brown [5] and Füredi [15] proved (1.8), whereas (1.9) was proved by Alon, Rónyai and Szabó [2]. Ball and Pepe [3] have recently proved that ex(n, K 5,5 ) ≫ n 7/4 . Their result also improves the exponent in the lower bound in (1.5) for the cases (ℓ 1 , ℓ 2 ) = (5, ℓ 2 ), 5 ≤ ℓ 2 ≤ 12 and for (ℓ 1 , ℓ 2 ) = (6, ℓ 2 ), 6 ≤ ℓ 2 ≤ 8.…”