Irreducibility of the Tutte polynomial of an embedded graph

Joanna Ellis-Monaghan; Andrew Goodall; Iain Moffatt; Steven Noble; Lluis Vena

doi:10.5802/alco.252

Irreducibility of the Tutte polynomial of an embedded graph

Joanna Ellis-Monaghan, Andrew Goodall, Iain Moffatt, Steven Noble, Lluis Vena

Research output: Contribution to journal › Article › peer-review

1 Downloads (Pure)

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	E-pub ahead of print - 19 Dec 2022

Access to Document

10.5802/alco.252Licence: CC BY

Cite this

@article{7d35950eca064517b31e99450fa49913,

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.",

author = "Joanna Ellis-Monaghan and Andrew Goodall and Iain Moffatt and Steven Noble and Lluis Vena",

year = "2022",

month = dec,

day = "19",

doi = "10.5802/alco.252",

language = "English",

volume = "5",

pages = "1337--1351",

journal = "Algebraic Combinatorics",

issn = "2589-5486",

publisher = "Centre Mersenne",

number = "6",

}

TY - JOUR

T1 - Irreducibility of the Tutte polynomial of an embedded graph

AU - Ellis-Monaghan, Joanna

AU - Goodall, Andrew

AU - Moffatt, Iain

AU - Noble, Steven

AU - Vena, Lluis

PY - 2022/12/19

Y1 - 2022/12/19

N2 - 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.

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.

U2 - 10.5802/alco.252

DO - 10.5802/alco.252

M3 - Article

SN - 2589-5486

VL - 5

SP - 1337

EP - 1351

JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

IS - 6

ER -