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.

中文翻译：

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关于格罗斯、曼苏尔和塔克的猜想

部分对偶性是带状图相对于它们的边子集的对偶性，概括了经典的欧拉-庞加莱对偶性。这个操作经常改变属。最近，JL Gross、T. Mansour 和 TW Tucker 提出了一个猜想，对于不同于平面树及其部分对偶的任何带状图，存在一个相对于它确实改变属的边部分对偶的子集。一族反例被齐焱和咸安金发现。在本笔记中，我们证明基本上这些是唯一的反例。