In 1988 Fellows conjectured that if a finite, connected graph admits a finite planar emulator, then it admits a finite planar cover. We construct a finite planar emulator for K4,5 − 4K2. Archdeacon [Dan Archdeacon, Two graphswithout planar covers, J. Graph Theory, 41 (4) (2002) 318–326] showed that K4,5−4K2 does not admit a finite planar cover; thusK4,5−4K2 provides a counterexample to Fellows’...

We answer a question raised by Lovász and B. Szegedy [Contractors and connectors in graph algebras, J. Graph Theory 60:1 (2009)] asking for a contractor for the graph parameter counting the number of B-flows of a graph, where B is a subset of a finite Abelian group closed under inverses. We prove our main result using the duality between flows and tensions and finite Fourier analysis.