The Same Upper Bound for Both: The 2-Page and the Rectilinear Crossing Numbers of the n-Cube

摘要

We present two main results: a 2-page drawing and a rectilinear drawing of the n-dimensional cube Q_n. Both drawings have the same number 125/768 4~n - 2~(n-3)/3 (3n~2+9+(-1)~(n+1)/2 of crossings, even though they are given by different constructions. The first improves the current best general 2-page drawing, while the second is the first non-trivial rectilinear drawing of Q_n.