  Partial duality is a duality of ribbon graphs relative to a subset of their
edges generalizing the classical Euler-Poincare duality. This operation often
changes the genus. Recently J.L.Gross, T.Mansour, and T.W.Tucker formulated a
conjecture that for any ribbon graph different from plane trees and their
partial duals, there is a subset of edges partial duality relative to which
does change the genus. A family of counterexamples was found by Qi Yan and
Xian'an Jin. In this note we prove that essentially these are the only
counterexamples.
