A characterization of circle graphs in terms of total unimodularity
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Abstract
A graph G has an associated multimatroid Z(3)(G), which is equivalent to the isotropic system of G studied by Bouchet. In previous work it was shown that G is a circle graph if and only if for every field F, the rank function of Z(3)(G) can be extended to the rank function of an F-representable matroid. In the present paper we strengthen this result using a multimatroid analogue of total unimodularity. As a consequence we obtain a characterization of matroid planarity in terms of this total-unimodularity analogue. (C)& nbsp;2021 Elsevier Ltd. All rights reserved.
Title
A characterization of circle graphs in terms of total unimodularity
Brijder, R. and L. Traldi (2022 May) "A characterization of circle graphs in terms of total unimodularity." European Journal of Combinatorics 102: 103455