Matroids, delta-matroids and embedded graphs. / Chun, Carolyn; Moffatt, Iain; Noble, Steven; Rueckriemen, Ralf.

In: Journal of Combinatorial Theory, Series A, Vol. 167, 10.2019, p. 7-59.

Research output: Contribution to journalArticle

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Matroids, delta-matroids and embedded graphs. / Chun, Carolyn; Moffatt, Iain; Noble, Steven; Rueckriemen, Ralf.

In: Journal of Combinatorial Theory, Series A, Vol. 167, 10.2019, p. 7-59.

Research output: Contribution to journalArticle

Harvard

Chun, C, Moffatt, I, Noble, S & Rueckriemen, R 2019, 'Matroids, delta-matroids and embedded graphs', Journal of Combinatorial Theory, Series A, vol. 167, pp. 7-59. https://doi.org/10.1016/j.jcta.2019.02.023

APA

Chun, C., Moffatt, I., Noble, S., & Rueckriemen, R. (2019). Matroids, delta-matroids and embedded graphs. Journal of Combinatorial Theory, Series A, 167, 7-59. https://doi.org/10.1016/j.jcta.2019.02.023

Vancouver

Chun C, Moffatt I, Noble S, Rueckriemen R. Matroids, delta-matroids and embedded graphs. Journal of Combinatorial Theory, Series A. 2019 Oct;167:7-59. https://doi.org/10.1016/j.jcta.2019.02.023

Author

Chun, Carolyn ; Moffatt, Iain ; Noble, Steven ; Rueckriemen, Ralf. / Matroids, delta-matroids and embedded graphs. In: Journal of Combinatorial Theory, Series A. 2019 ; Vol. 167. pp. 7-59.

BibTeX

@article{40c2ab42921a49ccbe90cb3dfb7ff2f4,
title = "Matroids, delta-matroids and embedded graphs",
abstract = "Matroid theory is often thought of as a generalization of graph theory. In this paper we propose an analogous correspondence between embedded graphs and delta-matroids. We show that delta-matroids arise as the natural extension of graphic matroids to the setting of embedded graphs. We show that various basic ribbon graph operations and concepts have delta-matroid analogues, and illus- trate how the connections between embedded graphs and delta-matroids can be exploited. Also, in direct analogy with the fact that the Tutte polynomial is matroidal, we show that several polynomials of embedded graphs from the literature, including the Las Vergnas, Bollabas-Riordan and Krushkal polynomials, are in fact delta-matroidal.",
author = "Carolyn Chun and Iain Moffatt and Steven Noble and Ralf Rueckriemen",
year = "2019",
month = "10",
doi = "10.1016/j.jcta.2019.02.023",
language = "English",
volume = "167",
pages = "7--59",
journal = "Journal of Combinatorial Theory, Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Matroids, delta-matroids and embedded graphs

AU - Chun, Carolyn

AU - Moffatt, Iain

AU - Noble, Steven

AU - Rueckriemen, Ralf

PY - 2019/10

Y1 - 2019/10

N2 - Matroid theory is often thought of as a generalization of graph theory. In this paper we propose an analogous correspondence between embedded graphs and delta-matroids. We show that delta-matroids arise as the natural extension of graphic matroids to the setting of embedded graphs. We show that various basic ribbon graph operations and concepts have delta-matroid analogues, and illus- trate how the connections between embedded graphs and delta-matroids can be exploited. Also, in direct analogy with the fact that the Tutte polynomial is matroidal, we show that several polynomials of embedded graphs from the literature, including the Las Vergnas, Bollabas-Riordan and Krushkal polynomials, are in fact delta-matroidal.

AB - Matroid theory is often thought of as a generalization of graph theory. In this paper we propose an analogous correspondence between embedded graphs and delta-matroids. We show that delta-matroids arise as the natural extension of graphic matroids to the setting of embedded graphs. We show that various basic ribbon graph operations and concepts have delta-matroid analogues, and illus- trate how the connections between embedded graphs and delta-matroids can be exploited. Also, in direct analogy with the fact that the Tutte polynomial is matroidal, we show that several polynomials of embedded graphs from the literature, including the Las Vergnas, Bollabas-Riordan and Krushkal polynomials, are in fact delta-matroidal.

U2 - 10.1016/j.jcta.2019.02.023

DO - 10.1016/j.jcta.2019.02.023

M3 - Article

VL - 167

SP - 7

EP - 59

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

SN - 0097-3165

ER -