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    The excluded 3-minors for vf-safe delta-matroids

    Bonin, J. and Chun, C. and Noble, Steven (2019) The excluded 3-minors for vf-safe delta-matroids. Advances in Applied Mathematics 126 (101909), ISSN 0196-8858.

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    Abstract

    Vf-safe delta-matroids have the desirable property of behaving well under certain duality operations. Several important classes of delta-matroids are known to be vf-safe, including the class of ribbon-graphic delta-matroids, which is related to the class of ribbon graphs or embedded graphs in the same way that graphic matroids correspond to graphs. In this paper, we characterize vf-safe delta-matroids and ribbon-graphic deltamatroids by finding the minimal obstructions, called excluded 3-minors, to membership in the class. We find the unique (up to twisted duality) excluded 3-minor within the class of set systems for the class of vf-safe delta-matroids. In the literature, binary delta-matroids appear in many different guises, with appropriate notions of minor operations equivalent to that of 3-minors, perhaps most notably as graphs with vertex minors. We give a direct explanation of this equivalence and show that some well-known results may be expressed in terms of 3-minors.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Steven Noble
    Date Deposited: 30 Apr 2019 15:50
    Last Modified: 02 Aug 2022 00:48
    URI: https://eprints.bbk.ac.uk/id/eprint/27347

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