Szymanski's conjecture

Statement

In mathematics, Szymanski's conjecture, named after Ted H. Szymanski, states that every permutation on the $n$-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths. That is, if the permutation $\sigma$ matches each vertex $v$ to another vertex $\sigma(v)$, then for each $v$ there exists a path in the hypercube graph from $v$ to $\sigma(v)$ such that no two paths for two different vertices $u$ and $v$ use the same edge in the same direction.