BIROn - Birkbeck Institutional Research Online

    On the interplay between embedded graphs and delta-matroids

    Chun, C. and Moffatt, I. and Noble, Steven and Rueckriemen, R. (2018) On the interplay between embedded graphs and delta-matroids. Proceedings of the London Mathematical Society 118 (3), pp. 675-700. ISSN 0024-6115.

    [img]
    Preview
    Text
    interplay_final_v1.pdf - Author's Accepted Manuscript

    Download (1MB) | Preview

    Abstract

    The mutually enriching relationship between graphs and matroids has motivated discoveries in both fields. In this paper, we exploit the similar relationship between embedded graphs and delta-matroids. There are well-known connections between geometric duals of plane graphs and duals of matroids. We obtain analogous connections for various types of duality in the literature for graphs in surfaces of higher genus and delta-matroids. Using this interplay, we establish a rough structure theorem for delta-matroids that are twists of matroids, we translate Petrie duality on ribbon graphs to loop complementation on delta-matroids, and we prove that ribbon graph polynomials, such as the Penrose polynomial, the characteristic polynomial, and the transition polynomial, are in fact delta-matroidal. We also express the Penrose polynomial as a sum of characteristic polynomials.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Steven Noble
    Date Deposited: 03 Sep 2018 08:34
    Last Modified: 24 Sep 2020 11:00
    URI: https://eprints.bbk.ac.uk/id/eprint/23754

    Statistics

    Downloads
    Activity Overview
    179Downloads
    81Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item