Castle–Evans–Hyde conjecture on nontrivial planar graph embeddings on the torus

Let $G$ be a planar graph embedded nontrivially on the torus. A nontrivial knot is a knotted embedded circle, and a nonsplit link is a nonsplit link with at least two components. Castle–Evans–Hyde conjecture. Every nontrivial embedding of a planar graph on the torus contains a nontrivial knot or a nonsplit link. This conjecture asserts that nontriviality for planar spatial graph embeddings on the torus must be detected by a knot or a nonsplit link.