A characterization of circle graphs in terms of total unimodularity. (May 2022) - Brijder, Robert; Traldi, Lorenzo
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.