论文标题
切片$ n $ -cube的所有边缘需要$ n^{2/3} $超平面
Slicing all Edges of an $n$-cube Requires $n^{2/3}$ Hyperplanes
论文作者
论文摘要
考虑带有顶点$ \ { - 1,1 \}^n $的$ n $ -Cube图，并将其连接到锤距$ 1 $的顶点的边缘。为了剖定所有边缘，需要$ \ mathbb {r}^n $中的多少个超平面？我们表明，至少需要$ \widetildeΩ（n^{2/3}）$，这改善了Yehuda和Yehudayoff的$ω（N^{0.51}）$的先前界限。
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 $\widetildeΩ(n^{2/3})$ are needed, which improves the previous bound of $Ω(n^{0.51})$ by Yehuda and Yehudayoff.
