On a conjecture of Gross, Mansour and Tucker
| Autor: | Fabien Vignes-Tourneret, Sergei Chmutov |
|---|---|
| Přispěvatelé: | Mathematics Department, The Ohio State University, Ohio State University [Columbus] (OSU), Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
05C10
05C65 57M15 57Q15 partial-dual genus polynomial Duality (optimization) Gross–Mansour–Tucker conjecture 0102 computer and information sciences 01 natural sciences Graph Ribbon graphs Combinatorics Mathematics - Geometric Topology Genus (mathematics) [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics 0101 mathematics Mathematics Conjecture Plane (geometry) 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology 010201 computation theory & mathematics Map Dual polyhedron Combinatorics (math.CO) Counterexample partial duality |
| Zdroj: | European Journal of Combinatorics European Journal of Combinatorics, Elsevier, 2021, 97, pp.103368. ⟨10.1016/j.ejc.2021.103368⟩ |
| ISSN: | 0195-6698 1095-9971 |
| DOI: | 10.1016/j.ejc.2021.103368⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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