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S\\'ark\\\"ozy, Mason DiCicco, Nathaniel Itty, Ryan Offstein","submitted_at":"2026-02-06T17:52:13Z","abstract_excerpt":"A collection of hyperplanes $\\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\\{-1,1\\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\\mathcal{H}$ intersecting $e$ in its interior. Let $S(n)$ be the minimum number of hyperplanes needed to slice $Q_n$. We prove that $S(n) \\leq \\lceil \\frac{4n}{5} \\rceil$, except when $n$ is an odd multiple of $5$, in which case $S(n) \\leq \\frac{4n}{5} +1$. This improves upon the previously known upper bound of $S(n) \\leq \\lceil\\frac{5n}{6} \\rceil$ due to Paterson reported in 1971. 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