Castle, Evans and Hyde's conjecture on polyhedral toroidal molecules

A polyhedral molecule has an underlying graph that is abstractly planar, 3-connected, and simple; a molecule is toroidal when its graph embedding on the standard torus does not embed on the sphere. Castle, Evans and Hyde's conjecture. All polyhedral toroidal molecules contain a nontrivial knot or a nonsplit link. This conjecture predicts that toroidal embeddings of sufficiently rigid abstractly planar molecular graphs cannot be ravel-like: their nonplanarity must be detected by a knot or a nonsplit link.