Claims

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1954_01_01_kovari_sos_turan: Kővári, Sós and Turán prove that the least number of ones in an n by n 0-1 matrix forcing a 2 by 2 minor of ones is asymptotic to n^{3/2}, which gives ex(n;K_{2,2}) >> n^{3/2}, the case r = 2; refereed in Colloq. Math. 3 (1954).

1966_02_01_erdos_renyi_sos: Erdős, Rényi and Sós prove that the largest number of edges of a graph on n vertices with no four-cycle is asymptotic to n^{3/2}/2, so ex(n;K_{2,2}) >> n^{3/2}, the case r = 2; refereed in Studia Sci. Math. Hungar. 1 (1966).

1966_08_01_brown: Brown's sphere graphs over GF(p) have no K_{3,3} and about n^{5/3}/2 edges, and his Section 3 gives the C_4 asymptotic, so ex(n;K_{r,r}) >> n^{2-1/r} holds for r = 3 and r = 2; a refereed paper in Canad. Math. Bull. 9 (1966).

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