Irreducibility of the Tutte polynomial of an embedded graph

Joanna A. Ellis-Monaghan; Andrew J. Goodall; Iain Moffatt; Steven D. Noble; Lluis Vena

doi:10.5802/alco.252

Irreducibility of the Tutte polynomial of an embedded graph

Joanna A. Ellis-Monaghan, Andrew J. Goodall, Iain Moffatt, Steven D. Noble, Lluis Vena

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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.

Original language	English
Pages (from-to)	1337-1351
Number of pages	15
Journal	Algebraic Combinatorics
Volume	5
Issue number	6
Early online date	19 Dec 2022
DOIs	https://doi.org/10.5802/alco.252
Publication status	Published - 2022

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10.5802/alco.252Licence: CC BY

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title = "Irreducibility of the Tutte polynomial of an embedded graph",

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.",

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AU - Goodall, Andrew J.

AU - Moffatt, Iain

AU - Noble, Steven D.

AU - Vena, Lluis

PY - 2022

Y1 - 2022

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AB - 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.

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DO - 10.5802/alco.252

M3 - Article

SN - 2589-5486

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EP - 1351

JO - Algebraic Combinatorics

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IS - 6

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