  Consider the $n$-cube graph with vertices $\{-1,1\}^n$ and edges connecting
vertices with hamming distance $1$. How many hyperplanes in $\mathbb{R}^n$ are
needed in order to dissect all edges? We show that at least
$\widetilde{\Omega}(n^{2/3})$ are needed, which improves the previous bound of
$\Omega(n^{0.51})$ by Yehuda and Yehudayoff.
