All Questions

Let $Q_n$ be the $n$-dimensional hypercube graph. How many vertex cycle covers exist on $Q_n$? (Presumably the best we can hope for are upper and lower bounds.) To be clear, a single "vertex cycle ...

Let $D$ be the digraph on $2^d$ vertices with $d2^d$ edges that we obtain by directing each edge of the $d$-dimensional hypercube in both directions. Can we partition the edges of $D$ into $d$ ...