Mayhew, D. orcid.org/0000-0003-4086-0980 and Probert, A. (2024) Supersolvable saturated matroids and chordal graphs. Advances in Applied Mathematics, 153. 102616. ISSN 0196-8858
Abstract
A matroid is supersolvable if it has a maximal chain of flats, each of which is modular. A matroid is saturated if every round flat is modular. In this article we present supersolvable saturated matroids as analogues to chordal graphs, and we show that several results for chordal graphs hold in this matroidal context. In particular, we consider matroid analogues of the reduced clique graph and clique trees for chordal graphs. The latter is a maximum-weight spanning tree of the former. We also show that the matroid analogue of a clique tree is an optimal decomposition for the matroid parameter of tree-width.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023, Elsevier Inc. 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. |
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: | 25 Jan 2024 11:22 |
Last Modified: | 18 Sep 2024 00:13 |
Published Version: | http://dx.doi.org/10.1016/j.aam.2023.102616 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aam.2023.102616 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208136 |