Types of embedded graphs and their Tutte polynomials. / Huggett, Stephen; Moffatt, Iain.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 169, No. 2, 09.2020, p. 255-297.

Research output: Contribution to journalArticle

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Types of embedded graphs and their Tutte polynomials. / Huggett, Stephen; Moffatt, Iain.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 169, No. 2, 09.2020, p. 255-297.

Research output: Contribution to journalArticle

Harvard

Huggett, S & Moffatt, I 2020, 'Types of embedded graphs and their Tutte polynomials', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 169, no. 2, pp. 255-297. https://doi.org/10.1017/S0305004119000161

APA

Huggett, S., & Moffatt, I. (2020). Types of embedded graphs and their Tutte polynomials. Mathematical Proceedings of the Cambridge Philosophical Society, 169(2), 255-297. https://doi.org/10.1017/S0305004119000161

Vancouver

Huggett S, Moffatt I. Types of embedded graphs and their Tutte polynomials. Mathematical Proceedings of the Cambridge Philosophical Society. 2020 Sep;169(2):255-297. https://doi.org/10.1017/S0305004119000161

Author

Huggett, Stephen ; Moffatt, Iain. / Types of embedded graphs and their Tutte polynomials. In: Mathematical Proceedings of the Cambridge Philosophical Society. 2020 ; Vol. 169, No. 2. pp. 255-297.

BibTeX

@article{5ffb630c81514d14bd85a54e6aaf689c,
title = "Types of embedded graphs and their Tutte polynomials",
abstract = "We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs on surfaces. We give a description of each class in terms of coloured ribbon graphs. We then iden- tify a universal deletion-contraction invariant (i.e., a {\textquoteleft}Tutte polynomial{\textquoteright}) for each class. We relate these to graph polynomials in the literature, including the Bollobas–Riordan, Krushkal, and Las Vergnas polynomials, and give state-sum formulations, duality rela- tions, deleton-contraction relations, and quasi-tree expansions for each of them.",
author = "Stephen Huggett and Iain Moffatt",
year = "2020",
month = sep,
doi = "10.1017/S0305004119000161",
language = "English",
volume = "169",
pages = "255--297",
journal = "Mathematical Proceedings of the Cambridge Philosophical Society",
issn = "0305-0041",
publisher = "Cambridge University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Types of embedded graphs and their Tutte polynomials

AU - Huggett, Stephen

AU - Moffatt, Iain

PY - 2020/9

Y1 - 2020/9

N2 - We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs on surfaces. We give a description of each class in terms of coloured ribbon graphs. We then iden- tify a universal deletion-contraction invariant (i.e., a ‘Tutte polynomial’) for each class. We relate these to graph polynomials in the literature, including the Bollobas–Riordan, Krushkal, and Las Vergnas polynomials, and give state-sum formulations, duality rela- tions, deleton-contraction relations, and quasi-tree expansions for each of them.

AB - We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs on surfaces. We give a description of each class in terms of coloured ribbon graphs. We then iden- tify a universal deletion-contraction invariant (i.e., a ‘Tutte polynomial’) for each class. We relate these to graph polynomials in the literature, including the Bollobas–Riordan, Krushkal, and Las Vergnas polynomials, and give state-sum formulations, duality rela- tions, deleton-contraction relations, and quasi-tree expansions for each of them.

U2 - 10.1017/S0305004119000161

DO - 10.1017/S0305004119000161

M3 - Article

VL - 169

SP - 255

EP - 297

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -