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http://hdl.handle.net/1942/30771
Title: | A Characterization of Circle Graphs in Terms of Multimatroid Representations | Authors: | BRIJDER, Robert Traldi, Lorenzo |
Issue Date: | 2020 | Publisher: | ELECTRONIC JOURNAL OF COMBINATORICS | Source: | ELECTRONIC JOURNAL OF COMBINATORICS, 27 (1) (Art N° P1.25) | Abstract: | The isotropic matroid M[IAS(G)] of a looped simple graph G is a binary matroid equivalent to the isotropic system of G. In general, M[IAS(G)] is not regular, so it cannot be represented over fields of characteristic not equal 2. The ground set of M[IAS(G)] is denoted W(G); it is partitioned into 3-element subsets corresponding to the vertices of G. When the rank function of M[IAS(G)] is restricted to subtransversals of this partition, the resulting structure is a multimatroid denoted Z(3)(G). In this paper we prove that G is a circle graph if and only if for every field F, there is an F-representable matroid with ground set W(G), which defines Z(3)(G) by restriction. We connect this characterization with several other circle graph characterizations that have appeared in the literature. | Notes: | Brijder, R (reprint author), Hasselt Univ, Hasselt, Belgium. robert.brijder@uhasselt.be; traldil@lafayette.edu |
Other: | Brijder, R (reprint author), Hasselt Univ, Hasselt, Belgium. robert.brijder@uhasselt.be; traldil@lafayette.edu | Document URI: | http://hdl.handle.net/1942/30771 | ISSN: | 1077-8926 | e-ISSN: | 1077-8926 | ISI #: | WOS:000513910100009 | Rights: | The authors. Released under the CC BY license (International 4.0). | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2021 |
Appears in Collections: | Research publications |
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