Abstract
Partial duality is a duality of ribbon graphs relative to a subset of their edges generalizing the classical Euler–Poincaré 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.
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