Proper-subset conjecture for classical spatial graphs in virtual spatial graph theory

A classical spatial graph is a spatial graph represented by a classical graph diagram, and two such graphs are virtually equivalent or classically equivalent according to the virtual or classical graph-diagram moves, respectively. Proper-subset conjecture. If two classical spatial graphs are virtually equivalent, then they are classically equivalent. This conjecture asserts that classical spatial graph theory embeds as a proper subset of virtual spatial graph theory; the source identifies the question as important but does not provide evidence of a resolution.