---
tag: GKZG0V1HQ0
kind: conjecture
name: Szymanski's conjecture
sources:
  - wikipedia: en:25435956@r1366108543
    locator: Szymanski's conjecture
    note: adopted
    mention: wikipedia://en/25435956
    sections: [Statement]
same_as:
  wikidata: Q7665039
  wikipedia: Szymanski's conjecture
inventory: [P3Z5AZKPS9]
---

## Statement

In mathematics, **Szymanski's conjecture**, named after Ted H. Szymanski, states that every [[permutation|05RWFKVTJ7]] on the $n$-dimensional doubly [[directed|0KFYGSHHF5]] hypercube graph can be routed with edge-disjoint [[paths|03NAMV1DHJ]]. 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.