On a conjecture of Gross, Mansour and Tucker
Combinatorics
2021-07-06 v2 Geometric Topology
Abstract
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.
Cite
@article{arxiv.2101.09319,
title = {On a conjecture of Gross, Mansour and Tucker},
author = {Sergei Chmutov and Fabien Vignes-Tourneret},
journal= {arXiv preprint arXiv:2101.09319},
year = {2021}
}