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

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

Published

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

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

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

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

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

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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",

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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.

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