Claims

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1992_07_01_chung: Chung's 1992 edge-partition of the n-cube into four subgraphs without a six-cycle, so a class with a quarter of the edges avoids C_6 and the statement fails for every epsilon at most 1/4; refereed and credited by the site.

1993_03_01_brouwer_dejter_thomassen: An explicit four-coloring of the n-cube's edges with no monochromatic four- or six-cycle, so a color class with a quarter of the edges avoids C_6 and the statement fails for every epsilon at most 1/4; refereed and credited.

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