Bonin, J.E., Chun, C. and Noble, S.D. orcid.org/0000-0002-1621-0059 (2021) The excluded 3-minors for vf-safe delta-matroids. Advances in Applied Mathematics, 126. 101909. ISSN 0196-8858
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 delta-matroids 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 |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article accepted for publication in Advances in Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Delta-matroid; Vf-safe; Excluded minor; Loop complementation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Mar 2025 11:55 |
Last Modified: | 14 Mar 2025 18:22 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aam.2019.04.006 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:224405 |
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