Can delta-star conversions be used to resolve any circuit of resistors into series and parallel combinations of resistors?

From Wikipedia: Every two-terminal network represented by a planar graph can be reduced to a single equivalent resistor by a sequence of series, parallel, $Y$-$Delta$, and $Delta$-$Y$ transformations. However, there are non-planar networks that cannot be simplified using these transformations, such as a regular square grid wrapped around a torus, or any member of the Petersen family.