Claims

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1966_01_01_benson: Benson's regular bipartite graphs of girth eight and twelve (Canad. J. Math. 1966) give ex(n; C_6) at least a constant times n^(4/3) and ex(n; C_10) at least a constant times n^(6/5): the instances k = 3 and 5.

1995_01_01_lazebnik_ustimenko_woldar: The q-regular bipartite graphs D(3,q) of girth at least eight (Bull. Amer. Math. Soc. 1995) give ex(n; C_6) at least a constant times n^(4/3), the instance k = 3; for k at least 4 their general bound is of smaller order.

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