Title: Slicing all edges of an n-cube requires n^{2/3} hyperplanes

Abstract:

Consider the n-cube graph in R^n, with vertices {0,1}^n and edges connecting vertices with Hamming distance 1.

How many hyperplanes are required in order to dissect all edges?

This problem has been open since the 70s. We will discuss this and related problems.

Puzzle: Show that n hyperplanes are sufficient, while sqrt(n) are not enough.