Claims

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1994_03_01_lazebnik_ustimenko_woldar: The site's first disproof: bipartite 2k-cycle-free graphs with constant 2/3^(4/3) at k = 3 and 4/5^(6/5) at k = 5, above the proposed 2^(-1-1/k); refereed in J. Combin. Theory Ser. B and credited by the site.

2005_06_10_furedi_naor_verstraete: An alternative disproof at k = 3: C_6-free bipartite graphs with parts m, 2m and 2m^(4/3) + O(m) edges, constant at least 2/3^(4/3) > 2^(-4/3) along a sequence of orders; refereed in Adv. Math., credited by the site.

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