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    Matroids, delta-matroids and embedded graphs

    Chun, C. and Moffatt, I. and Noble, Steven and Rueckriemen, R. (2019) Matroids, delta-matroids and embedded graphs. Journal of Combinatorial Theory, Series A 167 , pp. 7-59. ISSN 0097-3165.

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    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 illustrate 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, Bollabás-Riordan and Krushkal polynomials, are in fact delta-matroidal.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Steven Noble
    Date Deposited: 27 Mar 2019 15:41
    Last Modified: 09 Aug 2023 12:46


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