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

Can delta-star conversions be used to resolve any circuit of resistors into series and parallel combinations of resistors? I mean to say that if we do not utilize any other techniques like merging points with the same potential and so on, can we reduce any circuit to a simple one where all resistances are in some combination of parallel and series connections?

• Hint: think about non-planar circuits. – The Photon Apr 5 '17 at 18:52

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.