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Irreducibility of the Tutte polynomial of an embedded graph

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Bibliographic Details
Title: Irreducibility of the Tutte polynomial of an embedded graph
Authors: Ellis Monaghan, Joanna A., Goodall, Andrew, Moffatt, Iain, Noble, Steven D., Vena Cros, Lluís
Contributors: Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
Source: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Algebraic Combinatorics
Publication Status: Preprint
Publisher Information: Cellule MathDoc/Centre Mersenne, 2022.
Publication Year: 2022
Subject Terms: Combinatorial analysis, Classificació AMS::05 Combinatorics::05C Graph theory, Bollobás-Riordan polynomial, 0102 computer and information sciences, Configuracions i dissenys combinatòrics, 01 natural sciences, Separable, ribbon graph polynomial, Ribbon graph, Grafs, Graph polynomials, delta-matroid, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), Delta-matroid, FOS: Mathematics, Mathematics - Combinatorics, ribbon graph, Bollobás–Riordan polynomial, 0101 mathematics, Teoria de, Grafs, Teoria de, 05C31 (Primary) 05B35 (Secondary), Combinatorial aspects of matroids and geometric lattices, Classificació AMS::05 Combinatorics::05B Designs and configurations, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs, Graph theory, Tutte polynomial, Ribbon graph polynomial, Irreducible, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Combinatorics (math.CO), separable, irreducible
Description: We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that the Tutte polynomial of a graph is irreducible if and only if the graph is connected and non-separable.
Document Type: Article
File Description: application/pdf; application/xml
Language: English
ISSN: 2589-5486
DOI: 10.5802/alco.252
DOI: 10.48550/arxiv.2212.10920
Access URL: http://arxiv.org/abs/2212.10920
https://zbmath.org/7635160
https://doi.org/10.5802/alco.252
https://hdl.handle.net/11245.1/09821e84-cc79-4d02-a814-a0bfd2b82307
https://dare.uva.nl/personal/pure/en/publications/irreducibility-of-the-tutte-polynomial-of-an-embedded-graph(09821e84-cc79-4d02-a814-a0bfd2b82307).html
https://doi.org/10.5802/alco.252
https://hdl.handle.net/2117/384710
https://doi.org/10.5802/alco.252
Rights: CC BY
Accession Number: edsair.doi.dedup.....0f5e24c9d91301dbb8c2d736b20b60c5
Database: OpenAIRE
Description
Abstract:We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that the Tutte polynomial of a graph is irreducible if and only if the graph is connected and non-separable.
ISSN:25895486
DOI:10.5802/alco.252